Inradius of a Right Triangle
2013-12-31 01:47
This GeoGebra applet demonstrates the geometric construction and calculation of the inradius of a right triangle. By drawing the right triangle and its inscribed circle using commands like Distance, Midpoint, and Intersect, it visually illustrates the tangency between the incircle and the three sides. It dynamically calculates and displays the inradius, helping students understand the properties o
In collections
Polygons: Interactive GeoGebra Geometry Book
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="4.2" version="4.2.60.0" id="0ba872de-4735-4e7b-bd49-5f5da5f8cb35" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1382" height="744" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.1447178002894356" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1" size="400" window="613,22,700,550" />
<view id="4" toolbar="0 59 || 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 | 1011 || 1008 1009 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="1355" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="200" window="100,100,250,400" />
<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="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="70" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="true" items="0 39 59 | 1 501 67 , 5 19 , 72 | 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 | 30 29 54 32 31 33 | 17 26 62 73 , 14 66 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="true" cmd="true" top="false" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="12"/>
<graphicsSettings javaLatexFonts="false"/>
</gui>
<euclidianView>
<size width="1355" height="578"/>
<coordSystem xZero="398.555555555556" yZero="510.3333333333332" scale="22.2222222222222" yscale="22.222222222222165"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="13" 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="10"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="numeric" label="m">
<value val="5.0"/>
<show object="true" label="true"/>
<objColor r="255" g="127" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="1" max="5" absoluteScreenLocation="true" width="100.0" x="264.0" y="59.0" fixed="true" horizontal="true"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="n">
<value val="3.0"/>
<show object="true" label="true"/>
<objColor r="255" g="127" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="1" max="5" absoluteScreenLocation="true" width="100.0" x="122.0" y="60.0" fixed="false" horizontal="true"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<expression label="mn" exp="m * n" />
<element type="numeric" label="mn">
<value val="15.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<auxiliary val="true"/>
</element>
<expression label="A" exp="(2 * mn, 0)" type="point" />
<element type="point" label="A">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="30.0" y="0.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="B" exp="(0, abs(m^(2) - n^(2)))" type="point" />
<element type="point" label="B">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="16.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="C">
<show object="true" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="0.0" y="0.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="B" a1="C" a2="A"/>
<output a0="poly1" a1="a" a2="b" a3="c"/>
</command>
<element type="polygon" label="poly1">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.05"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="a">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="16.0" y="0.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="b">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="30.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="c">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-16.0" y="-30.0" z="480.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Distance">
<input a0="B" a1="C"/>
<output a0="distanceBC"/>
</command>
<element type="numeric" label="distanceBC">
<value val="16.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Midpoint">
<input a0="B" a1="C"/>
<output a0=""/>
</command>
<command name="Distance">
<input a0="C" a1="A"/>
<output a0="distanceCA"/>
</command>
<element type="numeric" label="distanceCA">
<value val="30.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Midpoint">
<input a0="C" a1="A"/>
<output a0=""/>
</command>
<command name="Distance">
<input a0="B" a1="A"/>
<output a0="distanceBA"/>
</command>
<element type="numeric" label="distanceBA">
<value val="34.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Midpoint">
<input a0="B" a1="A"/>
<output a0=""/>
</command>
<expression label="r" exp="(distanceBC - distanceBA + distanceCA) / 2" />
<element type="numeric" label="r">
<value val="6.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="D" exp="(r, r)" type="point" />
<element type="point" label="D">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="6.0" y="6.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="D" a1="r"/>
<output a0="d"/>
</command>
<element type="conic" label="d">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<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="36.0" A3="0.0" A4="-6.0" A5="-6.0"/>
<eqnStyle style="specific"/>
</element>
<command name="Intersect">
<input a0="d" a1="xAxis"/>
<output a0="E" a1=""/>
</command>
<element type="point" label="E">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="6.0" y="-0.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Distance">
<input a0="D" a1="E"/>
<output a0="distanceDE"/>
</command>
<element type="numeric" label="distanceDE">
<value val="6.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Midpoint">
<input a0="D" a1="E"/>
<output a0=""/>
</command>
<command name="Segment">
<input a0="D" a1="E"/>
<output a0="e"/>
</command>
<element type="segment" label="e">
<show object="true" label="false"/>
<objColor r="255" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="6.0" y="0.0" z="-36.0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Intersect">
<input a0="d" a1="yAxis"/>
<output a0="F" a1=""/>
</command>
<element type="point" label="F">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="6.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="D" a1="F"/>
<output a0="f"/>
</command>
<element type="segment" label="f">
<show object="true" label="false"/>
<objColor r="255" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-6.0" z="36.0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Intersect">
<input a0="d" a1="c"/>
<output a0="G" a1=""/>
</command>
<element type="point" label="G">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="8.823529411764707" y="11.294117647058822" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="D" a1="G"/>
<output a0="g"/>
</command>
<element type="segment" label="g">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-5.2941176470588225" y="2.8235294117647065" z="14.823529411764689"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="B" a1="F"/>
<output a0="h"/>
</command>
<element type="segment" label="h">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="10.0" y="0.0" z="0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="B" a1="G"/>
<output a0="i"/>
</command>
<element type="segment" label="i">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4.7058823529411775" y="8.823529411764707" z="-141.1764705882353"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="E" a1="A"/>
<output a0="j"/>
</command>
<element type="segment" label="j">
<show object="true" label="false"/>
<objColor r="0" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.0" y="24.0" z="0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="A" a1="G"/>
<output a0="k"/>
</command>
<element type="segment" label="k">
<show object="true" label="false"/>
<objColor r="0" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-11.294117647058822" y="-21.176470588235293" z="338.8235294117647"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="F" a1="C"/>
<output a0="l"/>
</command>
<element type="segment" label="l">
<show object="true" label="false"/>
<objColor r="255" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="6.0" y="0.0" z="0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="C" a1="E"/>
<output a0="p"/>
</command>
<element type="segment" label="p">
<show object="true" label="false"/>
<objColor r="255" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="6.0" z="-0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="文字DE_1" exp=""r= \, " + (LaTeX[distanceDE]) + """ />
<element type="text" label="文字DE_1">
<show object="true" label="false"/>
<objColor r="255" g="0" b="255" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1.4" size="5" style="1"/>
<startPoint exp="Midpoint[D, E]"/>
</element>
<expression label="文字BA" exp=""\overline{" + (Name[B]) + "" + (Name[A]) + "} \, = \, " + (LaTeX[distanceBA]) + """ />
<element type="text" label="文字BA">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1.4" size="5" style="1"/>
<startPoint exp="Midpoint[B, A]"/>
<labelOffset x="77" y="20"/>
</element>
<expression label="文字CA" exp=""\overline{" + (Name[C]) + "" + (Name[A]) + "} \, = \, " + (LaTeX[distanceCA]) + """ />
<element type="text" label="文字CA">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1.4" size="5" style="1"/>
<startPoint exp="Midpoint[C, A]"/>
<labelOffset x="-56" y="21"/>
</element>
<expression label="文字BC" exp=""\overline{" + (Name[B]) + "" + (Name[C]) + "} \, = \, " + (LaTeX[distanceBC]) + """ />
<element type="text" label="文字BC">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1.4" size="5" style="1"/>
<startPoint exp="Midpoint[B, C]"/>
</element>
<expression label="text1" exp=""m≠n""/>
<element type="text" label="text1">
<show object="true" label="false"/>
<objColor r="255" g="127" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="12" style="1"/>
<startPoint x="-11.00500000000003" y="17.92500000000004" z="1.0"/>
</element>
<expression label="text2" exp=""直角△ABC中，∠C=90°，\overline{BC}+\overline{CA}=\overline{BA}+2r""/>
<element type="text" label="text2">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="12" style="1"/>
<startPoint x="1.0549999999999855" y="21.885000000000048" z="1.0"/>
</element>
<expression label="text3" exp=""r=\frac{1}{2}(\overline{BC}+\overline{CA}-\overline{BA})=\frac{1}{2}(" + (LaTeX[distanceBC]) + "+" + (LaTeX[distanceCA]) + "-" + (LaTeX[distanceBA]) + ")=" + (LaTeX[0.5 * (distanceBC + distanceCA - distanceBA)]) + """ />
<element type="text" label="text3">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="12" style="1"/>
<startPoint x="4.434999999999988" y="19.035000000000004" z="1.0"/>
</element>
<expression label="text4" exp=""2013.12.31阿培製""/>
<element type="text" label="text4">
<show object="true" label="false"/>
<condition showObject="m * m + n * n ≟ 41"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="1"/>
<startPoint x="22.970000000000006" y="6.04500000000001" z="1.0"/>
</element>
</construction>
</geogebra>