Excenters of a Variable Triangle
2019-12-29 04:49
This GeoGebra applet demonstrates the geometric construction and dynamic properties of the excenters of a variable triangle. Using angle bisectors and related geometric commands, it accurately constructs the excenters. Users can drag the vertices to observe the dynamic changes and geometric properties of the excenters as the triangle's shape changes, making it an excellent tool for teaching and ex
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.570.0" app="classic" platform="d" id="7479ec7e-c97d-4143-a354-b60f6421980b" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1366" height="728" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.14641288433382138" 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 51 | 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="330" window="100,100,700,550" />
<view id="1" visible="true" inframe="false" stylebar="false" location="1" size="1134" window="100,100,600,400" />
<view id="2" visible="true" 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" toolbar="0" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" 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="1134" height="560"/>
<coordSystem xZero="365.00000000000017" yZero="270.0" scale="49.999999999999986" yscale="50.0"/>
<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>
<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"/>
<startAnimation val="true"/>
</kernel>
<tableview min="-2.0" max="2.0" step="1.0"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<command name="Intersect">
<input a0="xAxis" a1="yAxis"/>
<output a0="A_1"/>
</command>
<element type="point" label="A_1">
<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="0.0" y="-0.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<element type="point" label="B_1">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="3.0" y="-2.0" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="A_1" a1="B_1"/>
<output a0="c"/>
</command>
<element type="conic" label="c">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" 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="-13.000000000000002" A3="0.0" A4="-0.0" A5="0.0"/>
<eqnStyle style="specific"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="true" 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="true"/>
<coords x="2.20274655758076" y="-2.854453993860492" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="A">
<show object="true" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="4.28" y="2.04" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="B">
<show object="true" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="3.32" y="-2.74" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="A" a1="B" a2="C"/>
<output a0="t1" a1="c_1" a2="d" a3="e"/>
</command>
<element type="polygon" label="t1">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="c_1">
<show object="true" label="true"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="4.78" y="-0.9600000000000004" z="-18.5"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="d">
<show object="true" label="true"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0.11445399386049182" y="-1.1172534424192397" z="-3.4412616918455496"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="e">
<show object="true" label="true"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="-4.894453993860492" y="2.07725344241924" z="16.710666071187656"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="AngularBisector">
<input a0="B" a1="C" a2="A"/>
<output a0="f"/>
</command>
<element type="line" 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="-0.5937859766163752" y="0.8046230260026973" z="3.604719426056964"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="AngularBisector">
<input a0="C" a1="A" a2="B"/>
<output a0="g"/>
</command>
<element type="line" label="g">
<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="0.9553999207214295" y="-0.29531507155153186" z="-3.4866689147225935"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="AngularBisector">
<input a0="C" a1="B" a2="A"/>
<output a0="h"/>
</command>
<element type="line" label="h">
<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="-0.7402587338631224" y="-0.6723221005882277" z="0.6154964408138219"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<expression label="text1" exp=""变化的三角形的旁心G""/>
<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 x="-4.260000000000005" y="4.68" z="1.0"/>
</element>
<element type="point" label="F">
<show object="true" label="false"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-7.15" y="-4.5" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="I">
<show object="true" label="false" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-3.54" y="-4.62" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="image" label="pic1">
<file name="7f49b9a18e2e544b028bdec0b8b9684d/许兴华数学GGB制图08.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="F"/>
<startPoint number="1" exp="I"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<command name="LineBisector">
<input a0="d"/>
<output a0="i"/>
</command>
<element type="line" label="i">
<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="1.1172534424192397" y="0.11445399386049182" z="-2.764999999999999"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="LineBisector">
<input a0="c_1"/>
<output a0="j"/>
</command>
<element type="line" label="j">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.9600000000000004" y="4.78" z="-1.975000000000001"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Ray">
<input a0="C" a1="A"/>
<output a0="k"/>
</command>
<element type="ray" label="k">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-4.894453993860492" y="2.07725344241924" z="16.710666071187656"/>
<lineStyle thickness="5" type="15" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Ray">
<input a0="C" a1="B"/>
<output a0="l"/>
</command>
<element type="ray" label="l">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.11445399386049182" y="1.1172534424192397" z="3.4412616918455496"/>
<lineStyle thickness="5" type="15" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="k"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="true" label="true"/>
<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="5.3768615716362405" y="4.6244407766414435" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="AngularBisector">
<input a0="D" a1="A" a2="B"/>
<output a0="m"/>
</command>
<element type="line" label="m">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.29531507155153186" y="0.9553999207214295" z="-3.2129643445122724"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Point">
<input a0="l"/>
<output a0="E"/>
</command>
<element type="point" label="E">
<show object="true" label="true"/>
<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="4.161119065742583" y="-2.6538338422319043" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="AngularBisector">
<input a0="A" a1="B" a2="E"/>
<output a0="n"/>
</command>
<element type="line" label="n">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.6723221005882278" y="0.7402587338631224" z="4.260418304737872"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="n" a1="m"/>
<output a0="G"/>
</command>
<element type="point" label="G">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<trace val="true"/>
<coords x="6.448828228202702" y="0.9019812007144488" z="0.8609460425586922"/>
<pointSize val="7"/>
<pointStyle val="0"/>
</element>
<command name="OrthogonalLine">
<input a0="G" a1="c_1"/>
<output a0="p"/>
</command>
<element type="line" label="p">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.8265082008563449" y="4.115322083430549" z="-10.502345238489662"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="c_1" a1="p"/>
<output a0="H"/>
</command>
<element type="point" label="H">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="86.21570997241523" y="34.91080852413821" z="20.464687431620117"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="G" a1="H"/>
<output a0="q"/>
</command>
<element type="conic" label="q">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" 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="46.02839035679147" A3="0.0" A4="-7.490397666544909" A5="-1.0476628686668934"/>
<eqnStyle style="specific"/>
</element>
<command name="Intersect">
<input a0="q" a1="k"/>
<output a0="J" a1="L"/>
</command>
<element type="point" label="J">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4.413130765790099" y="2.3536845966990794" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<element type="point" label="L">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4.413130765790099" y="2.3536845966990794" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="q" a1="l"/>
<output a0="K" a1="M"/>
</command>
<element type="point" label="K">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="7.8310733944769115" y="-2.2778753405514705" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<element type="point" label="M">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="7.8310733944769115" y="-2.2778753405514705" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="G" a1="K"/>
<output a0="s"/>
</command>
<element type="segment" label="s">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.325538209218364" y="0.34067572793200274" z="-25.26651695274559"/>
<lineStyle thickness="5" type="15" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="G" a1="H"/>
<output a0="t"/>
</command>
<element type="segment" label="t">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.6582419315304116" y="-3.277496284078505" z="8.364204986980178"/>
<lineStyle thickness="5" type="15" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="G" a1="J"/>
<output a0="a"/>
</command>
<element type="segment" label="a">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.306021728032186" y="-3.07726690075481" z="13.006560373007698"/>
<lineStyle thickness="5" type="15" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
</construction>
</geogebra>