Distance Between Chords and the Centre of a Circle
2016-12-05 06:35
This applet demonstrates the distance between chords and a circle's center. By constructing chords and perpendiculars from the center, it illustrates the perpendicular chord bisector theorem. Users can explore the relationship among chord length, radius, and center-to-chord distance via the Pythagorean theorem, serving as an ideal interactive tool for learning plane geometry.
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.299.0" id="359f8b46-0812-4786-96fc-dc7b258c109a" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1022" height="923" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.0" orientation="1" />
</panes>
<views>
<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="200" window="0,0,400,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="1006" window="0,0,400,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="200" window="0,0,200,400" />
<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" size="150" window="50,50,500,500" />
<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="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="4097" visible="false" inframe="true" stylebar="true" location="1" size="150" 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="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" size="300" 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="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="20"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1006" height="708"/>
<coordSystem xZero="50.42546536737289" yZero="331.7167831788741" scale="34.859498378653235" yscale="34.85949837865325"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="1" rightAngleStyle="1" checkboxSize="13" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="64" g="64" b="64"/>
<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" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="point" label="O">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-11" y="-3"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="6.72857518942536" y="2.199793153033571" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="B_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="8.966696285682556" y="-3.335768505846711" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="O" a1="B_1"/>
<output a0="c"/>
</command>
<element type="conic" label="c">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<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="14.461185075106972" A3="0.0" A4="-6.72857518942536" A5="-2.199793153033571"/>
<eqnStyle style="specific"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="true" label="true"/>
<objColor r="0" g="0" b="204" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-16" y="-4"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="3.6743837769563434" y="7.330440649868395" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="true" label="true"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="0" y="6"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="12.6055369708285" y="3.2547572001478606" z="1.0"/>
<pointSize val="3"/>
<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="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-14" y="31"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="6.582828329600358" y="-3.7693262773035436" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="true" label="true"/>
<objColor r="0" g="0" b="204" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-18" y="29"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="2.325595113040322" y="-1.8332448293977053" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="A" a1="B"/>
<output a0="a"/>
</command>
<element type="segment" label="a">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="9.1636854792661" y="-1.3487886639160216" z="-23.783682012094086"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="C" a1="D"/>
<output a0="b"/>
</command>
<element type="segment" label="b">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="7.024083477451404" y="-6.022708641228141" z="-68.93988964676926"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="OrthogonalLine">
<input a0="O" a1="a"/>
<output a0="d"/>
</command>
<element type="line" label="d">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.3487886639160216" y="9.1636854792661" z="-29.233638513646245"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="a" a1="d"/>
<output a0="M"/>
</command>
<element type="point" label="M">
<show object="true" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-29" y="9"/>
<labelMode val="0"/>
<coords x="257.3761817299338" y="235.80870806951845" z="85.79236242282074"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="M" a1="O"/>
<output a0="e"/>
</command>
<element type="segment" label="e">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.5488047572017742" y="3.7285857444270274" z="-11.89479146423562"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="OrthogonalLine">
<input a0="O" a1="b"/>
<output a0="f"/>
</command>
<element type="line" label="f">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="6.022708641228141" y="7.024083477451404" z="-55.97577867653923"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="b" a1="f"/>
<output a0="N"/>
</command>
<element type="point" label="N">
<show object="true" label="true"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="2" y="22"/>
<labelMode val="0"/>
<coords x="821.3653457398618" y="-22.026326961555924" z="85.61076807532993"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="O" a1="N"/>
<output a0="g"/>
</command>
<element type="segment" label="g">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.457077691611413" y="2.86560746078907" z="-22.8363756657928"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Angle">
<input a0="O" a1="M" a2="A"/>
<output a0="α"/>
</command>
<element type="angle" label="α">
<angleStyle val="0"/>
<value val="1.5707963267948968"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<layer val="0"/>
<labelOffset x="20" y="-3"/>
<labelMode val="2"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<arcSize val="30"/>
</element>
<command name="Angle">
<input a0="O" a1="N" a2="C"/>
<output a0="β"/>
</command>
<element type="angle" label="β">
<angleStyle val="1"/>
<value val="4.71238898038469"/>
<show object="true" label="true"/>
<objColor r="255" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelOffset x="-17" y="-21"/>
<labelMode val="2"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<arcSize val="30"/>
</element>
<command name="Distance">
<input a0="A" a1="B"/>
<output a0="distanceAB"/>
</command>
<element type="numeric" label="distanceAB">
<value val="9.262416662125535"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="TextAB" exp=""\overline{" + (Name[A]) + (Name[B]) + "} \, = \, " + distanceAB" />
<element type="text" label="TextAB">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1.0" size="0" style="0"/>
<absoluteScreenLocation x="566" y="150"/>
</element>
<command name="Distance">
<input a0="C" a1="D"/>
<output a0="distanceCD"/>
</command>
<element type="numeric" label="distanceCD">
<value val="9.25260871729319"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="TextCD" exp=""\overline{" + (Name[C]) + (Name[D]) + "} \, = \, " + distanceCD" />
<element type="text" label="TextCD">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1.0" size="0" style="0"/>
<absoluteScreenLocation x="564" y="207"/>
</element>
<command name="Distance">
<input a0="M" a1="O"/>
<output a0="distanceMO"/>
</command>
<element type="numeric" label="distanceMO">
<value val="3.768758192703765"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Distance">
<input a0="O" a1="N"/>
<output a0="distanceON"/>
</command>
<element type="numeric" label="distanceON">
<value val="3.7747764042317065"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="TextON" exp=""\overline{" + (Name[O]) + (Name[N]) + "} \, = \, " + distanceON" />
<element type="text" label="TextON">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1.0" size="0" style="0"/>
<absoluteScreenLocation x="565" y="344"/>
</element>
<command name="Distance">
<input a0="O" a1="M"/>
<output a0="distanceOM"/>
</command>
<element type="numeric" label="distanceOM">
<value val="3.768758192703765"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="TextOM" exp=""\overline{" + (Name[O]) + (Name[M]) + "} \, = \, " + distanceOM" />
<element type="text" label="TextOM">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1.0" size="0" style="0"/>
<absoluteScreenLocation x="561" y="288"/>
</element>
</construction>
</geogebra>