Interactive 3D Conic Sections Model
2017-11-09 06:46
This 3D GeoGebra model demonstrates conic sections. By adjusting the intersecting plane, users observe curves like ellipses, parabolas, and hyperbolas generated when a plane intersects a cone. Using commands like Cone, Plane, Intersect, and Locus, it illustrates the geometric generation of conic sections, serving as a great visualization tool for solid and coordinate geometry.
In collections
Interactive Conic Sections Gallery
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.396.0" app="classic" platform="w" id="5c8385c4-7d42-4e2d-8c4a-77f5791bc87b" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1920" height="949" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.171875" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1,1" size="400" window="610,245,700,550" />
<view id="1" visible="false" inframe="false" stylebar="true" location="3,1,3" size="404" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="true" location="1,1" size="300" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3,3" size="246" window="100,100,250,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="16" visible="true" inframe="false" stylebar="false" location="3" size="330" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="2" size="332" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="true" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502 | 100001" visible="true" inframe="false" stylebar="false" location="1" size="1582" window="100,100,600,400" />
</views>
<toolbar show="true" items="0 39 73 62 | 1 501 67 , 5 19 , 72 75 76 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6 ||" position="1" help="false" />
<input show="true" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="24"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="404" height="763"/>
<coordSystem xZero="266" yZero="577" scale="49.99999999999998" yscale="50.00000000000003"/>
<evSettings axes="true" grid="true" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<euclidianView>
<viewNumber viewNo="2"/>
<size width="330" height="896"/>
<coordSystem xZero="363.586125" yZero="234.63437499999992" scale="62.08125000000007" yscale="62.081249999999976"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<bgColor r="255" g="250" b="205"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<kernel>
<uses3D val="true"/>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<euclidianView3D>
<coordSystem xZero="1.9796503429706567" yZero="-0.3492343269533045" zZero="-0.060363907423345076" scale="23.958764627963777" xAngle="8" zAngle="243"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" gridType="3"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="2" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<plate show="false"/>
<bgColor r="255" g="255" b="255"/>
<clipping use="false" show="false" size="1"/>
<projection type="0"/>
</euclidianView3D>
<construction title="圓錐截痕模型" author="" date="">
<element type="numeric" label="c">
<value val="2.48"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="-77" y="-18"/>
<labelMode val="3"/>
<slider min="-8" max="8" absoluteScreenLocation="true" width="200" x="57" y="270" fixed="true" horizontal="false" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.01" speed="1" type="0" playing="false"/>
<ggbscript onUpdate="SetActiveView[-1] ZoomIn[1] SetVisibleInView(d_1,-1,false) SetVisibleInView(b,-1,true)"/>
<caption val="上下"/>
</element>
<element type="numeric" label="a">
<value val="-2.6"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="-9" y="53"/>
<labelMode val="3"/>
<slider min="-8" max="8" absoluteScreenLocation="true" width="200" x="59" y="271" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<ggbscript onUpdate="SetActiveView[-1] ZoomIn[1] SetVisibleInView(d_1,-1,false) SetVisibleInView(b,-1,true)"/>
<caption val="左右"/>
</element>
<expression label="C" exp="(a, 0, 0)" type="point" />
<element type="point3d" label="C">
<show object="false" label="true" ev="7"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="-2.6" y="0" z="0" w="1"/>
<pointSize val="1"/>
</element>
<expression label="D" exp="(a, 1, 0)" type="point" />
<element type="point3d" label="D">
<show object="false" label="true" ev="7"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="-2.6" y="1" z="0" w="1"/>
<pointSize val="1"/>
</element>
<expression label="B" exp="(0, 0, c)" type="point" />
<element type="point3d" label="B">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="0" y="0" z="2.48" w="1"/>
<pointSize val="1"/>
</element>
<command name="Plane">
<input a0="B" a1="C" a2="D"/>
<output a0="b"/>
</command>
<element type="plane3d" label="b">
<show object="true" label="false" ev="4"/>
<objColor r="99" g="219" b="219" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="2.48" y="0" z="-2.6" w="6.448"/>
<fading val="0.1"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
</element>
<element type="numeric" label="d">
<value val="7"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="-29" y="59"/>
<labelMode val="3"/>
<slider min="0" max="10" absoluteScreenLocation="true" width="200" x="53" y="359" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<ggbscript onUpdate="SetActiveView[-1] ZoomIn[1]"/>
<caption val="圓錐半徑"/>
</element>
<command name="Point">
<input a0="zAxis"/>
<output a0="E"/>
</command>
<element type="point3d" label="E">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<coords x="0" y="0" z="-11.06088164084108" w="1"/>
<pointSize val="1"/>
</element>
<command name="Intersect">
<input a0="xAxis" a1="yAxis"/>
<output a0="O"/>
</command>
<element type="point" label="O">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelOffset x="-38" y="12"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="0" y="0" z="1"/>
<coordStyle style="cartesian3d"/>
<pointSize val="1"/>
<pointStyle val="0"/>
</element>
<command name="Cone">
<input a0="E" a1="O" a2="d"/>
<output a0="e" a1="f" a2="g"/>
</command>
<element type="quadriclimited" label="e">
<show object="true" label="false" ev="4"/>
<objColor r="153" g="51" b="0" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
</element>
<element type="conic3d" label="f">
<show object="false" label="false" ev="4"/>
<objColor r="153" g="51" b="0" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-49.00000000000001" A3="0" A4="0" A5="0"/>
<eqnStyle style="implicit"/>
</element>
<element type="quadricpart" label="g">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="255" b="0" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="1"/>
</element>
<command name="Point">
<input a0="f"/>
<output a0="G"/>
</command>
<element type="point3d" label="G">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="1" y="-3"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<isShape val="false"/>
<coords x="6.977771648112525" y="-0.5574072360465253" z="-11.06088164084108" w="1"/>
<pointSize val="1"/>
</element>
<command name="Line">
<input a0="O" a1="G"/>
<output a0="h"/>
</command>
<element type="line3d" label="h">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="0" oy="0" oz="0" ow="1" vx="6.977771648112525" vy="-0.5574072360465253" vz="-11.06088164084108" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="Intersect">
<input a0="h" a1="b"/>
<output a0="A"/>
</command>
<element type="point3d" label="A">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<trace val="true"/>
<isShape val="false"/>
<coords x="-0.9767602954699897" y="0.07802680913543338" z="1.5483209489363177" w="1"/>
<pointSize val="2"/>
</element>
<command name="Locus">
<input a0="A" a1="G"/>
<output a0="loc1"/>
</command>
<element type="locus" label="loc1">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
</element>
<expression label="text1" exp=""\shadowbox{截面方向}""/>
<element type="text" label="text1">
<show object="true" label="false" ev="43"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="109" y="132"/>
</element>
<element type="boolean" label="i">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="42" y="456"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="StartAnimation(G,i)"/>
<caption val="動態軌跡"/>
</element>
<command name="OrthogonalLine">
<input a0="O" a1="b"/>
<output a0="j"/>
</command>
<element type="line3d" label="j">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="0" oy="0" oz="0" ow="1" vx="2.48" vy="0" vz="-2.6" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="Point">
<input a0="j"/>
<output a0="F"/>
</command>
<element type="point3d" label="F">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<coords x="41.0786269472956" y="0" z="-43.06630244474538" w="1"/>
<pointSize val="1"/>
</element>
<command name="Vector">
<input a0="F" a1="O"/>
<output a0="u"/>
</command>
<element type="vector3d" label="u">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="-41.0786269472956" y="0" z="43.06630244474538" w="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<startPoint exp="F"/>
</element>
<element type="button" label="button1">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="47" y="512"/>
<labelMode val="0"/>
<fixed val="true"/>
<isShape val="false"/>
<auxiliary val="true"/>
<ggbscript val="SetViewDirection(-u)"/>
<font serif="false" sizeM="2" size="24" style="0"/>
<caption val="視角切換"/>
</element>
<command name="IntersectPath">
<input a0="b" a1="e"/>
<output a0="k"/>
</command>
<element type="conic3dpart" label="k">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="0.33280804620109417" A1="1" A2="-2.463315000325394" A3="0" A4="0.6855673124332913" A5="0"/>
<eqnStyle style="implicit"/>
</element>
<command name="Corner">
<input a0="k"/>
<output a0="H" a1="I" a2="L" a3="M"/>
</command>
<element type="point3d" label="H">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<element type="point3d" label="I">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<element type="point3d" label="L">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<element type="point3d" label="M">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<command name="Cone">
<input a0="(-E)" a1="O" a2="d"/>
<output a0="g'" a1="g'_2" a2="g'_3"/>
</command>
<element type="quadriclimited" label="g'">
<show object="true" label="false" ev="4"/>
<objColor r="153" g="51" b="0" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
</element>
<element type="conic3d" label="g'_2">
<show object="false" label="false" ev="4"/>
<objColor r="153" g="51" b="0" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-49.00000000000001" A3="0" A4="0" A5="0"/>
<eqnStyle style="implicit"/>
</element>
<element type="quadricpart" label="g'_3">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="255" b="0" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="-1" z1="0" x2="0" y2="0" z2="-1"/>
</element>
<command name="IntersectPath">
<input a0="b" a1="g'"/>
<output a0="p"/>
</command>
<element type="conic3dpart" label="p">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="0.33280804620109417" A1="1" A2="-2.463315000325394" A3="0" A4="0.6855673124332913" A5="0"/>
<eqnStyle style="implicit"/>
</element>
<command name="Corner">
<input a0="p"/>
<output a0="J" a1="K" a2="N" a3="P"/>
</command>
<element type="point3d" label="J">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<element type="point3d" label="K">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<element type="point3d" label="N">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<element type="point3d" label="P">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<command name="Center">
<input a0="k"/>
<output a0="Q"/>
</command>
<element type="point3d" label="Q">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<command name="Midpoint">
<input a0="H" a1="I"/>
<output a0="R"/>
</command>
<element type="point3d" label="R">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="1"/>
<pointSize val="1"/>
</element>
<command name="Line">
<input a0="R" a1="Q"/>
<output a0="l"/>
</command>
<element type="line3d" label="l">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="-3.2760197518163903" oy="4.440892098500626e-16" oz="-11.06088164084108" ow="1" vx="2.5733247204175824" vy="-4.440892098500626e-16" vz="10.636408844392674" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="Intersect">
<input a0="l" a1="g"/>
<output a0="S" a1="T"/>
</command>
<element type="point3d" label="S">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="-0.4340627766093088" y="-4.6358970876536204e-17" z="0.6858738566815248" w="1"/>
<pointSize val="1"/>
</element>
<element type="point3d" label="T">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="-0.9713272861883064" y="4.6358970876536105e-17" z="-1.5348194495783325" w="1"/>
<pointSize val="1"/>
</element>
<command name="Midpoint">
<input a0="J" a1="K"/>
<output a0="U"/>
</command>
<element type="point3d" label="U">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="1"/>
<pointSize val="1"/>
</element>
<command name="AngularBisector">
<input a0="O" a1="T" a2="R"/>
<output a0="m"/>
</command>
<element type="line3d" label="m">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="-0.9713272861883064" oy="4.6358970876536105e-17" oz="-1.5348194495783325" ow="1" vx="NaN" vy="NaN" vz="NaN" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="Intersect">
<input a0="zAxis" a1="m"/>
<output a0="V"/>
</command>
<element type="point3d" label="V">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<command name="OrthogonalLine">
<input a0="V" a1="b"/>
<output a0="n"/>
</command>
<element type="line3d" label="n">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="NaN" oy="NaN" oz="NaN" ow="1" vx="2.48" vy="0" vz="-2.6" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="Intersect">
<input a0="n" a1="b"/>
<output a0="W"/>
</command>
<element type="point3d" label="W">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="2"/>
<caption val="F"/>
</element>
<command name="Sphere">
<input a0="V" a1="W"/>
<output a0="o"/>
</command>
<element type="quadric" label="o">
<show object="true" label="false" ev="4"/>
<condition showObject="c_1"/>
<objColor r="204" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="1"/>
<matrix A0="1" A1="1" A2="1" A3="NaN" A4="0" A5="0" A6="0" A7="NaN" A8="NaN" A9="NaN"/>
</element>
<command name="AngularBisector">
<input a0="O" a1="S" a2="U"/>
<output a0="q"/>
</command>
<element type="line3d" label="q">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="-0.4340627766093088" oy="-4.6358970876536204e-17" oz="0.6858738566815248" ow="1" vx="NaN" vy="NaN" vz="NaN" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="Intersect">
<input a0="zAxis" a1="q"/>
<output a0="Z"/>
</command>
<element type="point3d" label="Z">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<command name="OrthogonalLine">
<input a0="Z" a1="b"/>
<output a0="r"/>
</command>
<element type="line3d" label="r">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="NaN" oy="NaN" oz="NaN" ow="1" vx="2.48" vy="0" vz="-2.6" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="Intersect">
<input a0="r" a1="b"/>
<output a0="A_1"/>
</command>
<element type="point3d" label="A_1">
<show object="true" label="true" ev="4"/>
<condition showObject="Q ∈ l"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="2"/>
<caption val="F"/>
</element>
<command name="Sphere">
<input a0="Z" a1="A_1"/>
<output a0="s"/>
</command>
<element type="quadric" label="s">
<show object="true" label="false" ev="4"/>
<condition showObject="c_1 ∧ Q ∈ l"/>
<objColor r="204" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="1"/>
<matrix A0="1" A1="1" A2="1" A3="NaN" A4="0" A5="0" A6="0" A7="NaN" A8="NaN" A9="NaN"/>
</element>
<command name="Center">
<input a0="p"/>
<output a0="B_1"/>
</command>
<element type="point3d" label="B_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="1.4905954244565418" y="0" z="3.9017987125585476" w="1"/>
<pointSize val="1"/>
</element>
<command name="OrthogonalLine">
<input a0="O" a1="b"/>
<output a0="f_1"/>
</command>
<element type="line3d" label="f_1">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="0" oy="0" oz="0" ow="1" vx="2.48" vy="0" vz="-2.6" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="Intersect">
<input a0="f_1" a1="b"/>
<output a0="C_1"/>
</command>
<element type="point3d" label="C_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="-1.2386169289874829" y="0" z="1.2985500061965547" w="1"/>
<pointSize val="1"/>
</element>
<command name="Line">
<input a0="Q" a1="C_1"/>
<output a0="t"/>
</command>
<element type="line3d" label="t">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="-0.702695031398808" oy="0" oz="-0.4244727964484061" ow="1" vx="0.13587271633368136" vy="0" vz="0.5616072275125497" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="Line">
<input a0="C_1" a1="B_1"/>
<output a0="g_1"/>
</command>
<element type="line3d" label="g_1">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="-1.2386169289874829" oy="0" oz="1.2985500061965547" ow="1" vx="2.7292123534440247" vy="0" vz="2.6032487063619927" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="Intersect">
<input a0="t" a1="k"/>
<output a0="D_1" a1="E_1"/>
</command>
<element type="point3d" label="D_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelOffset x="15" y="25"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<element type="point3d" label="E_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<command name="Intersect">
<input a0="t" a1="p"/>
<output a0="F_1" a1="G_1"/>
</command>
<element type="point3d" label="F_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelOffset x="33" y="2"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<element type="point3d" label="G_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<command name="Intersect">
<input a0="g_1" a1="p"/>
<output a0="H_1" a1="I_1"/>
</command>
<element type="point3d" label="H_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="3.9598914421502056" y="0" z="6.257127221743273" w="1"/>
<pointSize val="1"/>
</element>
<element type="point3d" label="I_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="-0.9787005932371219" y="0" z="1.5464702033738222" w="1"/>
<pointSize val="1"/>
</element>
<command name="Mirror">
<input a0="O" a1="H_1"/>
<output a0="O'"/>
</command>
<element type="point3d" label="O'">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="7.919782884300411" y="0" z="12.514254443486546" w="1"/>
<pointSize val="1"/>
</element>
<command name="AngularBisector">
<input a0="B_1" a1="H_1" a2="O'"/>
<output a0="h_1"/>
</command>
<element type="line3d" label="h_1">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="3.9598914421502056" oy="0" oz="6.257127221743273" ow="1" vx="-0.1888410755080756" vy="0" vz="0.15478853151713945" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="AngularBisector">
<input a0="B_1" a1="H_1" a2="O"/>
<output a0="i_1"/>
</command>
<element type="line3d" label="i_1">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="3.9598914421502056" oy="0" oz="6.257127221743273" ow="1" vx="-1.2583753885585167" vy="0" vz="-1.535210389549889" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="Intersect">
<input a0="h_1" a1="zAxis"/>
<output a0="J_1"/>
</command>
<element type="point3d" label="J_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="-4.440892098500626e-16" y="0" z="9.502955914725408" w="1"/>
<pointSize val="1"/>
</element>
<command name="Intersect">
<input a0="i_1" a1="zAxis"/>
<output a0="K_1"/>
</command>
<element type="point3d" label="K_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="0" y="0" z="1.4260835294134697" w="1"/>
<pointSize val="1"/>
</element>
<command name="OrthogonalLine">
<input a0="J_1" a1="b"/>
<output a0="j_1"/>
</command>
<element type="line3d" label="j_1">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="-4.440892098500626e-16" oy="0" oz="9.502955914725408" ow="1" vx="2.48" vy="0" vz="-2.6" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="OrthogonalLine">
<input a0="K_1" a1="b"/>
<output a0="k_1"/>
</command>
<element type="line3d" label="k_1">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="0" oy="0" oz="1.4260835294134697" ow="1" vx="2.48" vy="0" vz="-2.6" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="Intersect">
<input a0="j_1" a1="b"/>
<output a0="L_1"/>
</command>
<element type="point3d" label="L_1">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<isShape val="false"/>
<coords x="3.507561325609542" y="0" z="5.825673879812179" w="1"/>
<pointSize val="2"/>
<caption val="F"/>
</element>
<command name="Intersect">
<input a0="k_1" a1="b"/>
<output a0="M_1"/>
</command>
<element type="point3d" label="M_1">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<isShape val="false"/>
<coords x="-0.5263704766964578" y="0" z="1.9779235453049173" w="1"/>
<pointSize val="2"/>
<caption val="F"/>
</element>
<command name="Sphere">
<input a0="J_1" a1="L_1"/>
<output a0="v"/>
</command>
<element type="quadric" label="v">
<show object="true" label="false" ev="4"/>
<condition showObject="c_1"/>
<objColor r="204" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="1"/>
<matrix A0="1" A1="1" A2="1" A3="64.48078150000727" A4="0" A5="0" A6="0" A7="4.440892098500626e-16" A8="0" A9="-9.502955914725408"/>
</element>
<command name="Sphere">
<input a0="K_1" a1="M_1"/>
<output a0="w"/>
</command>
<element type="quadric" label="w">
<show object="true" label="false" ev="4"/>
<condition showObject="c_1"/>
<objColor r="204" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="1"/>
<matrix A0="1" A1="1" A2="1" A3="1.4521209509876494" A4="0" A5="0" A6="0" A7="0" A8="0" A9="-1.4260835294134697"/>
</element>
<command name="Mirror">
<input a0="O" a1="D_1"/>
<output a0="O'_1"/>
</command>
<element type="point3d" label="O'_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<command name="AngularBisector">
<input a0="O" a1="D_1" a2="Q"/>
<output a0="l_1"/>
</command>
<element type="line3d" label="l_1">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="NaN" oy="NaN" oz="NaN" ow="1" vx="NaN" vy="NaN" vz="NaN" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="AngularBisector">
<input a0="Q" a1="D_1" a2="O'_1"/>
<output a0="m_1"/>
</command>
<element type="line3d" label="m_1">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="NaN" oy="NaN" oz="NaN" ow="1" vx="NaN" vy="NaN" vz="NaN" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="Intersect">
<input a0="l_1" a1="zAxis"/>
<output a0="N_1"/>
</command>
<element type="point3d" label="N_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<command name="Intersect">
<input a0="zAxis" a1="m_1"/>
<output a0="O_1"/>
</command>
<element type="point3d" label="O_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<command name="OrthogonalLine">
<input a0="O_1" a1="b"/>
<output a0="n_1"/>
</command>
<element type="line3d" label="n_1">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="NaN" oy="NaN" oz="NaN" ow="1" vx="2.48" vy="0" vz="-2.6" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="OrthogonalLine">
<input a0="N_1" a1="b"/>
<output a0="p_1"/>
</command>
<element type="line3d" label="p_1">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="NaN" oy="NaN" oz="NaN" ow="1" vx="2.48" vy="0" vz="-2.6" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="Intersect">
<input a0="n_1" a1="b"/>
<output a0="P_1"/>
</command>
<element type="point3d" label="P_1">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="2"/>
<caption val="F"/>
</element>
<command name="Intersect">
<input a0="p_1" a1="b"/>
<output a0="Q_1"/>
</command>
<element type="point3d" label="Q_1">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="2"/>
<caption val="F"/>
</element>
<command name="Sphere">
<input a0="N_1" a1="Q_1"/>
<output a0="a_1"/>
</command>
<element type="quadric" label="a_1">
<show object="true" label="false" ev="4"/>
<condition showObject="c_1"/>
<objColor r="255" g="192" b="203" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="1"/>
<matrix A0="1" A1="1" A2="1" A3="NaN" A4="0" A5="0" A6="0" A7="NaN" A8="NaN" A9="NaN"/>
</element>
<command name="Sphere">
<input a0="O_1" a1="P_1"/>
<output a0="b_1"/>
</command>
<element type="quadric" label="b_1">
<show object="true" label="false" ev="4"/>
<condition showObject="c_1"/>
<objColor r="255" g="192" b="203" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="1"/>
<matrix A0="1" A1="1" A2="1" A3="NaN" A4="0" A5="0" A6="0" A7="NaN" A8="NaN" A9="NaN"/>
</element>
<element type="boolean" label="c_1">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="41" y="420"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="內切球"/>
</element>
<element type="button" label="button2">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="47" y="618"/>
<labelMode val="0"/>
<fixed val="true"/>
<isShape val="false"/>
<auxiliary val="true"/>
<ggbscript val="SetVisibleInView(d_1,-1,false) SetVisibleInView(b,-1,true) SetValue(a,0) SetValue(c,6)"/>
<font serif="false" sizeM="2" size="24" style="0"/>
<caption val="交會直線"/>
</element>
<element type="button" label="button4">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="266" y="619"/>
<labelMode val="0"/>
<fixed val="true"/>
<isShape val="false"/>
<auxiliary val="true"/>
<ggbscript val="SetVisibleInView(d_1,-1,false) SetVisibleInView(b,-1,true) SetValue(c,0) SetValue(a,5)"/>
<font serif="false" sizeM="2" size="24" style="0"/>
<caption val="點"/>
</element>
<command name="Intersect">
<input a0="b" a1="f"/>
<output a0="R_1" a1="S_1"/>
</command>
<element type="point3d" label="R_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<element type="point3d" label="S_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<command name="Intersect">
<input a0="b" a1="g'_2"/>
<output a0="T_1" a1="U_1"/>
</command>
<element type="point3d" label="T_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<element type="point3d" label="U_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
<pointSize val="1"/>
</element>
<command name="Intersect">
<input a0="h" a1="f" a2="1"/>
<output a0="W_1"/>
</command>
<element type="point3d" label="W_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="6.977771648112525" y="-0.5574072360465253" z="-11.06088164084108" w="1"/>
<pointSize val="1"/>
</element>
<command name="Line">
<input a0="U_1" a1="S_1"/>
<output a0="r_1"/>
</command>
<element type="line3d" label="r_1">
<show object="true" label="false" ev="4"/>
<condition showObject="V_1 ∈ b ∧ O ∈ b"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<coords ox="2.07601975181639" oy="6.6850685852927665" oz="11.06088164084108" ow="1" vx="-5.35203950363278" vy="-12.871157380784542" vz="-22.12176328168216" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="Line">
<input a0="T_1" a1="R_1"/>
<output a0="q_1"/>
</command>
<element type="line3d" label="q_1">
<show object="true" label="false" ev="4"/>
<condition showObject="V_1 ∈ b ∧ O ∈ b"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<coords ox="2.07601975181639" oy="-6.685068585292766" oz="11.06088164084108" ow="1" vx="-5.35203950363278" vy="12.871157380784542" vz="-22.12176328168216" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="Midpoint">
<input a0="U_1" a1="T_1"/>
<output a0="V_1"/>
</command>
<element type="point3d" label="V_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN" w="1"/>
<pointSize val="1"/>
</element>
<command name="Center">
<input a0="g'_2"/>
<output a0="F_2"/>
</command>
<element type="point3d" label="F_2">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="0" y="0" z="11.06088164084108" w="1"/>
<pointSize val="1"/>
</element>
<command name="OrthogonalLine">
<input a0="F_2" a1="h" a2="space"/>
<output a0="t_1"/>
</command>
<element type="line3d" label="t_1">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="0" oy="0" oz="11.06088164084108" ow="1" vx="0.8423161826258763" vy="-0.06728697339382729" vz="0.5347671565252207" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="OrthogonalPlane">
<input a0="A" a1="t_1"/>
<output a0="d_1"/>
</command>
<element type="plane3d" label="d_1">
<show object="true" label="false" ev="11"/>
<objColor r="99" g="219" b="219" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="0.8423161826258763" y="-0.06728697339382729" z="0.5347671565252207" w="-1.1102230246251565e-16"/>
<fading val="0.1"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
</element>
<element type="button" label="button3">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="180" y="618"/>
<labelMode val="0"/>
<fixed val="true"/>
<isShape val="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue(c,0) SetValue(a,5) SetVisibleInView(b,-1,false) SetVisibleInView(d_1,-1,true)"/>
<font serif="false" sizeM="2" size="24" style="0"/>
<caption val="直線"/>
</element>
<expression label="text2" exp=""\underline{退化情形\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ }""/>
<element type="text" label="text2">
<show object="true" label="false" ev="43"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint x="-5.131760797342188" y="-5.353719923487368" z="1"/>
</element>
</construction>
</geogebra>