计算圆弧长度
2019-05-14 00:53
本范例演示了如何计算圆的圆弧长度。通过构造圆、点、射线和圆弧,结合旋转和交点等几何操作,直观地展示了圆弧的几何特征及其长度的计算方法。适用于学习圆的基本性质和弧长公式的几何意义。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.504.0" app="classic" platform="d" id="7c5c2e5b-333e-4dd3-b3ad-1894b9cb8078" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1069" height="717" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.18709073900841908" orientation="1" />
</panes>
<views>
<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" visible="false" inframe="false" stylebar="false" location="1,1,1" size="500" 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="false" location="1,1" size="300" window="100,100,600,400" />
<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="4097" visible="false" inframe="false" stylebar="true" location="1,1" size="370" window="100,100,700,550" />
<view id="1" visible="true" inframe="false" stylebar="false" location="1" size="1050" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="200" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="70" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
</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="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="12"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1050" height="568"/>
<coordSystem xZero="265.99999999999994" yZero="319.0000000000001" scale="50.0" yscale="50.00000000000003"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<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="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<spreadsheetView>
<prefCellSize height="24"/>
</spreadsheetView>
<algebraView>
<mode val="3"/>
</algebraView>
<kernel>
<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"/>
<construction title="" author="" date="">
<element type="numeric" label="r">
<value val="4.0"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="2" max="5" width="4.0" x="10.000000000000002" y="3.000000000000001" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="point" label="O">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="3.0" y="1.0" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="1"/>
</element>
<command name="Circle">
<input a0="O" a1="r"/>
<output a0="c"/>
</command>
<element type="conic" label="c">
<show object="true" label="false"/>
<objColor r="64" g="64" b="64" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="9" type="15" typeHidden="1" opacity="178"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="-6.0" A3="0.0" A4="-3.0" A5="-1.0"/>
<eqnStyle style="specific"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-1.0" y="1.0000000000000004" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Ray">
<input a0="B" a1="O"/>
<output a0="f"/>
</command>
<element type="ray" label="f">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4.440892098500626E-16" y="4.0" z="-4.000000000000002"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="numeric" label="n">
<value val="1.0"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="1" max="4" width="4.0" x="10.000000000000002" y="-0.9999999999999972" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<command name="Intersect">
<input a0="c" a1="f" a2="2"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="true" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="7.0" y="0.9999999999999997" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Rotate">
<input a0="C" a1="(n * 90°)" a2="O"/>
<output a0="C'"/>
</command>
<element type="point" label="C'">
<show object="true" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.0000000000000004" y="5.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="CircleArc">
<input a0="O" a1="C" a2="C'"/>
<output a0="d"/>
</command>
<element type="conicpart" label="d">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="13" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="-6.0" A3="0.0" A4="-3.0" A5="-1.0"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="O" a1="C"/>
<output a0="g"/>
</command>
<element type="segment" label="g">
<show object="true" label="false" ev="4"/>
<condition showObject="a ≤ 1"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="3.3306690738754696E-16" y="4.0" z="-4.000000000000001"/>
<lineStyle thickness="8" type="15" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Midpoint">
<input a0="O" a1="C"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="5.0" y="0.9999999999999998" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="text1" exp=""" + r + " cm"" />
<element type="text" label="text1">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<startPoint exp="A"/>
<labelOffset x="-23" y="34"/>
</element>
<command name="Circle">
<input a0="O" a1="r"/>
<output a0="e"/>
</command>
<element type="conic" label="e">
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 4"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="13" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="-6.0" A3="0.0" A4="-3.0" A5="-1.0"/>
<eqnStyle style="specific"/>
</element>
<expression label="text2" exp=""半徑長度""/>
<element type="text" label="text2">
<symbolic val="true" />
<show object="true" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="false" sizeM="2.0" size="12" style="1"/>
<startPoint x="10.08" y="4.3" z="1.0"/>
</element>
<expression label="text3" exp=""\frac{" + (LaTeX[n]) + "}{4}個圓的弧線"" />
<element type="text" label="text3">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="12" style="1"/>
<startPoint x="10.1" y="1.3599999999999999" z="1.0"/>
</element>
<element type="numeric" label="a">
<value val="0.0"/>
<show object="true" label="true"/>
<condition showObject="b"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="3" absoluteScreenLocation="true" width="200.0" x="766.0" y="519.0" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="point" label="D">
<show object="true" label="false" ev="4"/>
<condition showObject="a ≟ 1"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="3.0" y="3.0" z="1.0"/>
<pointSize val="8"/>
<pointStyle val="3"/>
</element>
<expression label="D1" exp="D + (0, r / 2)" type="point" />
<element type="point" label="D1">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <coords x="3.0" y="5.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="D2" exp="D - (0, r / 2)" type="point" />
<element type="point" label="D2">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.0" y="1.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="D1" a1="D2"/>
<output a0="h"/>
</command>
<element type="segment" label="h">
<show object="true" label="false" ev="4"/>
<condition showObject="a ≟ 1"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="4.0" y="0.0" z="-12.0"/>
<lineStyle thickness="13" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="point" label="E">
<show object="true" label="false" ev="4"/>
<condition showObject="a ≟ 1"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="5.0" y="1.0" z="1.0"/>
<pointSize val="7"/>
<pointStyle val="3"/>
</element>
<expression label="E1" exp="E + (r / 2, 0)" type="point" />
<element type="point" label="E1">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="7.0" y="1.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="E2" exp="E - (r / 2, 0)" type="point" />
<element type="point" label="E2">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.0" y="1.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="E2" a1="E1"/>
<output a0="i"/>
</command>
<element type="segment" label="i">
<show object="true" label="false" ev="4"/>
<condition showObject="a ≟ 1"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="4.0" z="-4.0"/>
<lineStyle thickness="13" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="text1_1" exp=""" + r + " cm"" />
<element type="text" label="text1_1">
<show object="false" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<startPoint exp="A"/>
<labelOffset x="-23" y="34"/>
</element>
<element type="point" label="E_1">
<show object="true" label="false" ev="4"/>
<condition showObject="a ≟ 2"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="1.0" y="1.0" z="1.0"/>
<pointSize val="7"/>
<pointStyle val="3"/>
</element>
<expression label="E1_1" exp="E_1 + (r / 2, 0)" type="point" />
<element type="point" label="E1_1">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.0" y="1.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="E2_1" exp="E_1 - (r / 2, 0)" type="point" />
<element type="point" label="E2_1">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.0" y="1.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="E2_1" a1="E1_1"/>
<output a0="i_1"/>
</command>
<element type="segment" label="i_1">
<show object="true" label="false" ev="4"/>
<condition showObject="a ≟ 2"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="4.0" z="-4.0"/>
<lineStyle thickness="13" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="text1_2" exp=""" + r + " cm"" />
<element type="text" label="text1_2">
<show object="false" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<startPoint exp="A"/>
<labelOffset x="-23" y="34"/>
</element>
<element type="point" label="E_2">
<show object="true" label="false" ev="4"/>
<condition showObject="a ≟ 2"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="5.0" y="1.0" z="1.0"/>
<pointSize val="7"/>
<pointStyle val="3"/>
</element>
<expression label="E1_2" exp="E_2 + (r / 2, 0)" type="point" />
<element type="point" label="E1_2">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="7.0" y="1.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="E2_2" exp="E_2 - (r / 2, 0)" type="point" />
<element type="point" label="E2_2">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.0" y="1.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="E2_2" a1="E1_2"/>
<output a0="i_2"/>
</command>
<element type="segment" label="i_2">
<show object="true" label="false" ev="4"/>
<condition showObject="a ≟ 2"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="4.0" z="-4.0"/>
<lineStyle thickness="13" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="text1_3" exp=""" + r + " cm"" />
<element type="text" label="text1_3">
<show object="false" label="true" ev="40"/>
<condition showObject="a ≟ 3"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<startPoint exp="A"/>
<labelOffset x="-23" y="34"/>
</element>
<element type="point" label="D_1">
<show object="true" label="false" ev="4"/>
<condition showObject="a ≟ 3"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="3.0" y="-1.0" z="1.0"/>
<pointSize val="8"/>
<pointStyle val="3"/>
</element>
<expression label="D1_1" exp="D_1 + (0, r / 2)" type="point" />
<element type="point" label="D1_1">
<show object="false" label="false" ev="4"/>
<condition showObject="a ≟ 3"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <coords x="3.0" y="1.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="D2_1" exp="D_1 - (0, r / 2)" type="point" />
<element type="point" label="D2_1">
<show object="false" label="false" ev="4"/>
<condition showObject="a ≟ 3"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.0" y="-3.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="D1_1" a1="D2_1"/>
<output a0="h_1"/>
</command>
<element type="segment" label="h_1">
<show object="true" label="false" ev="4"/>
<condition showObject="a ≟ 3"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="4.0" y="0.0" z="-12.0"/>
<lineStyle thickness="13" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="text1_4" exp=""" + r + " cm"" />
<element type="text" label="text1_4">
<show object="false" label="true" ev="40"/>
<condition showObject="a ≟ 3"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<startPoint exp="A"/>
<labelOffset x="-23" y="34"/>
</element>
<expression label="text1_5" exp=""" + r + " cm"" />
<element type="text" label="text1_5">
<show object="false" label="true" ev="40"/>
<condition showObject="a ≟ 3"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<startPoint exp="A"/>
<labelOffset x="-23" y="34"/>
</element>
<expression label="text1_6" exp=""" + r + " cm"" />
<element type="text" label="text1_6">
<show object="false" label="true" ev="40"/>
<condition showObject="a ≟ 3"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<startPoint exp="A"/>
<labelOffset x="-23" y="34"/>
</element>
<element type="point" label="E_3">
<show object="true" label="false" ev="4"/>
<condition showObject="a ≟ 3"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="5.0" y="1.0" z="1.0"/>
<pointSize val="7"/>
<pointStyle val="3"/>
</element>
<expression label="E1_3" exp="E_3 + (r / 2, 0)" type="point" />
<element type="point" label="E1_3">
<show object="false" label="false" ev="4"/>
<condition showObject="a ≟ 3"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="7.0" y="1.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="E2_3" exp="E_3 - (r / 2, 0)" type="point" />
<element type="point" label="E2_3">
<show object="false" label="false" ev="4"/>
<condition showObject="a ≟ 3"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.0" y="1.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="E2_3" a1="E1_3"/>
<output a0="i_3"/>
</command>
<element type="segment" label="i_3">
<show object="true" label="false" ev="4"/>
<condition showObject="a ≟ 3"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="4.0" z="-4.0"/>
<lineStyle thickness="13" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="text1_7" exp=""" + r + " cm"" />
<element type="text" label="text1_7">
<show object="false" label="true" ev="40"/>
<condition showObject="a ≟ 3"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<startPoint exp="A"/>
<labelOffset x="-23" y="34"/>
</element>
<expression label="text1_8" exp=""" + r + " cm"" />
<element type="text" label="text1_8">
<show object="false" label="true" ev="40"/>
<condition showObject="a ≟ 3"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<startPoint exp="A"/>
<labelOffset x="-23" y="34"/>
</element>
<expression label="text1_9" exp=""" + r + " cm"" />
<element type="text" label="text1_9">
<show object="false" label="true" ev="40"/>
<condition showObject="a ≟ 3"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<startPoint exp="A"/>
<labelOffset x="-23" y="34"/>
</element>
<expression label="text1_{10}" exp=""" + r + " cm"" />
<element type="text" label="text1_{10}">
<show object="false" label="true" ev="40"/>
<condition showObject="a ≟ 3"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<startPoint exp="A"/>
<labelOffset x="-23" y="34"/>
</element>
<expression label="text1_{11}" exp=""" + r + " cm"" />
<element type="text" label="text1_{11}">
<show object="false" label="true" ev="40"/>
<condition showObject="a ≟ 3"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<startPoint exp="A"/>
<labelOffset x="-23" y="34"/>
</element>
<element type="boolean" label="b">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="761" y="445"/>
<labelMode val="4"/>
<checkbox fixed="true"/>
<caption val="顯示直線"/>
</element>
</construction>
</geogebra>