Tangential Quadrilateral
2017-10-30 06:53
This applet demonstrates the geometric construction and fundamental properties of a tangential quadrilateral. Using GeoGebra, users can intuitively observe the tangency between the sides of the quadrilateral and the inscribed circle, and measure side lengths and related distances to verify classic geometric properties such as the sum of opposite sides being equal. Ideal for teaching and exploring
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.394.0" app="classic" platform="d" id="a5ae9d61-4477-48aa-b2bc-3ac3562e06d2" 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="1,1,1,1" size="400" window="478,88,700,550" />
<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="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="100,100,600,400" />
<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="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 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="1355" height="573"/>
<coordSystem xZero="466.0000000000001" yZero="391.9999999999999" scale="50.0" yscale="49.99999999999998"/>
<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>
<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="">
<command name="Intersect">
<input a0="xAxis" a1="yAxis"/>
<output a0="A"/>
</command>
<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"/>
<isShape val="false"/>
<coords x="0.0" y="-0.0" z="1.0"/>
<pointSize val="4"/>
<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="1" speed="1" type="1" playing="false"/>
<isShape val="false"/>
<coords x="2.46" y="-0.12" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="A" a1="B"/>
<output a0="c"/>
</command>
<element type="conic" label="c">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="9" 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="-6.065999999999999" 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"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<isShape val="false"/>
<coords x="2.1209060861999722" y="1.252101183419261" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="c"/>
<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="1" speed="1" type="1" playing="false"/>
<isShape val="false"/>
<coords x="-1.2671645048504712" y="2.111940841417453" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="c"/>
<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="1" speed="1" type="1" playing="false"/>
<isShape val="false"/>
<coords x="-1.4610047943031057" y="-1.9827922208399291" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="F"/>
</command>
<element type="point" label="F">
<show object="true" label="true"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<isShape val="false"/>
<coords x="1.2700367182807584" y="-2.110214854989567" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="A" a1="E"/>
<output a0="f"/>
</command>
<element type="segment" label="f">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="1.9827922208399291" y="-1.4610047943031057" z="-0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="A" a1="D"/>
<output a0="g"/>
</command>
<element type="segment" label="g">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="-2.111940841417453" y="-1.2671645048504712" z="0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="A" a1="C"/>
<output a0="h"/>
</command>
<element type="segment" label="h">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="-1.252101183419261" y="2.1209060861999722" z="0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="A" a1="F"/>
<output a0="i"/>
</command>
<element type="segment" label="i">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="2.110214854989567" y="1.2700367182807584" z="0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="OrthogonalLine">
<input a0="E" a1="f"/>
<output a0="j"/>
</command>
<element type="line" label="j">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="1.4610047943031057" y="1.9827922208399291" z="6.065999999999999"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="OrthogonalLine">
<input a0="D" a1="g"/>
<output a0="k"/>
</command>
<element type="line" label="k">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="1.2671645048504712" y="-2.111940841417453" z="6.066"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="OrthogonalLine">
<input a0="C" a1="h"/>
<output a0="l"/>
</command>
<element type="line" label="l">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="-2.1209060861999722" y="-1.252101183419261" z="6.065999999999998"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="OrthogonalLine">
<input a0="F" a1="i"/>
<output a0="m"/>
</command>
<element type="line" label="m">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="-1.2700367182807584" y="2.110214854989567" z="6.065999999999998"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="m" a1="l"/>
<output a0="G"/>
</command>
<element type="point" label="G">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="20.395809088987946" y="-5.161373585797949" z="6.065782007082218"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="l" a1="k"/>
<output a0="H"/>
</command>
<element type="point" label="H">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="5.215787365417031" y="20.552036205311985" z="6.065846360366724"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="k" a1="j"/>
<output a0="I"/>
</command>
<element type="point" label="I">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="-24.83865075565328" y="1.1758351958196815" z="5.598079617337429"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="j" a1="m"/>
<output a0="J"/>
</command>
<element type="point" label="J">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="-0.7729456987517054" y="-16.566497815333715" z="5.601252945337551"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="J" a1="F"/>
<output a0="n"/>
</command>
<element type="segment" label="n">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="-0.8474265829182794" y="1.4080318608488334" z="4.04751262541522"/>
<lineStyle thickness="13" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="J" a1="E"/>
<output a0="p"/>
</command>
<element type="segment" label="p">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="-0.9748492170679175" y="-1.3230096517350307" z="-4.047512625415219"/>
<lineStyle thickness="13" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="G" a1="F"/>
<output a0="q"/>
</command>
<element type="segment" label="q">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="1.2593149084086168" y="-2.0924001555097" z="-6.0147900642963625"/>
<lineStyle thickness="13" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="G" a1="C"/>
<output a0="r"/>
</command>
<element type="segment" label="r">
<show object="true" label="false"/>
<objColor r="255" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="-2.1030011300002114" y="-1.2415307875904862" z="6.0147900642963625"/>
<lineStyle thickness="13" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="H" a1="D"/>
<output a0="s"/>
</command>
<element type="segment" label="s">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="1.2762155648502236" y="-2.127025941417041" z="6.109328020748954"/>
<lineStyle thickness="13" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="H" a1="C"/>
<output a0="t"/>
</command>
<element type="segment" label="t">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="2.136055222848416" y="1.2610446496334022" z="-6.109328020748953"/>
<lineStyle thickness="13" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="I" a1="E"/>
<output a0="a"/>
</command>
<element type="segment" label="a">
<show object="true" label="false"/>
<objColor r="0" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="2.1928348204803636" y="2.9759901135090647" z="9.104512232198912"/>
<lineStyle thickness="13" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="I" a1="D"/>
<output a0="b"/>
</command>
<element type="segment" label="b">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="-1.901898241777019" y="3.1698304029616997" z="-9.104512232198914"/>
<lineStyle thickness="13" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Distance">
<input a0="H" a1="I"/>
<output a0="distanceHI"/>
</command>
<element type="numeric" label="distanceHI">
<value val="6.177142907595713"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Midpoint">
<input a0="H" a1="I"/>
<output a0=""/>
</command>
<expression label="文字HI" exp="Name[H] + (Name[I]) + " = " + distanceHI" />
<element type="text" label="文字HI">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="1"/>
<startPoint exp="Midpoint[H, I]"/>
<labelOffset x="-64" y="-48"/>
</element>
<command name="Distance">
<input a0="J" a1="G"/>
<output a0="distanceJG"/>
</command>
<element type="numeric" label="distanceJG">
<value val="4.085509027333821"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Midpoint">
<input a0="J" a1="G"/>
<output a0=""/>
</command>
<expression label="文字JG" exp="Name[J] + (Name[G]) + " = " + distanceJG" />
<element type="text" label="文字JG">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="1"/>
<startPoint exp="Midpoint[J, G]"/>
<labelOffset x="9" y="38"/>
</element>
<command name="Distance">
<input a0="J" a1="I"/>
<output a0="distanceJI"/>
</command>
<element type="numeric" label="distanceJI">
<value val="5.340001979710023"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Midpoint">
<input a0="J" a1="I"/>
<output a0=""/>
</command>
<expression label="文字JI" exp="Name[J] + (Name[I]) + " = " + distanceJI" />
<element type="text" label="文字JI">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="1"/>
<startPoint exp="Midpoint[J, I]"/>
<labelOffset x="-61" y="52"/>
</element>
<command name="Distance">
<input a0="H" a1="G"/>
<output a0="distanceHG"/>
</command>
<element type="numeric" label="distanceHG">
<value val="4.9226499552195095"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Midpoint">
<input a0="H" a1="G"/>
<output a0=""/>
</command>
<expression label="文字HG" exp="Name[H] + (Name[G]) + " = " + distanceHG" />
<element type="text" label="文字HG">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="1"/>
<startPoint exp="Midpoint[H, G]"/>
<labelOffset x="14" y="-47"/>
</element>
<expression label="text1" exp=""圓外切四邊形GHIJ, \overline{IH}+\overline{JG}=\overline{JI}+\overline{HG}=" + (LaTeX[distanceHI + distanceJG]) + """ />
<element type="text" label="text1">
<show object="true" label="false" ev="8"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="4.0" size="36" style="1"/>
<startPoint x="-8.940000000000001" y="6.520000000000001" z="1.0"/>
</element>
</construction>
</geogebra>