Basic Concepts of a Circle
2013-03-21 03:18
This GeoGebra applet demonstrates the basic concepts and geometric constructions of a circle. Through the interaction of fundamental geometric elements such as points, segments, circle arcs, and lines, it visually illustrates core properties including the center, radius, arc, chord, and intersections between lines and circles. This model helps students gain a deeper understanding of the definition
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="4.2" version="4.2.25.0" id="a399da11-805d-4f33-b051-2a26ed1e25a4" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="957" height="752" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.26332288401253917" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1" size="400" window="-969,268,700,550" />
<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="200" window="0,0,400,400" />
<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="957" 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="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" toolbar="0 || 2020 || 2021 || 2022" 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="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="20"/>
<graphicsSettings javaLatexFonts="false"/>
</gui>
<euclidianView>
<size width="957" height="614"/>
<coordSystem xZero="214.99999999999994" yZero="315.00000000000006" scale="49.99999999999998" yscale="50.00000000000002"/>
<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="圓的基本概念" author="JACK" date=" 18 March 2013">
<worksheetText above="圓周： 圓心： 半徑： 直徑： 弦VS孤 弦： 劣弧： 優弧： 扇形VS弓形" below=""/>
<element type="numeric" label="radius">
<value val="3.1"/>
<show object="true" label="true"/>
<objColor r="75" g="0" b="130" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="1" max="10" absoluteScreenLocation="true" width="100.0" x="120.0" y="35.0" fixed="false" horizontal="true"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<element type="point" label="A">
<show object="true" label="true"/>
<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="3.52" y="0.34" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="A" a1="radius"/>
<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="1"/>
<lineStyle thickness="4" 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="2.8959999999999986" A3="0.0" A4="-3.52" A5="-0.34"/>
<eqnStyle style="specific"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="true" label="true"/>
<objColor r="51" g="51" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-9" y="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="3.2951393430856535" y="3.431834032572261" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="A" a1="B"/>
<output a0="r"/>
</command>
<element type="segment" label="r">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-4" y="15"/>
<labelMode val="0"/>
<coords x="-3.0918340325722613" y="-0.22486065691434654" z="10.959708418005238"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="true" label="true"/>
<objColor r="0" g="204" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-20" y="36"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="0.7719473537347019" y="-1.0946451315061478" 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="0" g="204" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="1" y="33"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="5.940693309273394" y="-1.5965546474187153" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="C" a1="A"/>
<output a0="a"/>
</command>
<element type="segment" label="a">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.434645131506148" y="2.748052646265298" z="4.115612963171439"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="A" a1="D"/>
<output a0="b"/>
</command>
<element type="segment" label="b">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.9365546474187154" y="2.420693309273394" z="-7.639708084066832"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Angle">
<input a0="C" a1="A" a2="D"/>
<output a0="ca"/>
</command>
<element type="angle" label="ca">
<value val="1.9857131748947852"/>
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<arcSize val="30"/>
<allowReflexAngle val="true"/>
</element>
<command name="CircleArc">
<input a0="A" a1="C" a2="D"/>
<output a0="arc"/>
</command>
<element type="conicpart" label="arc">
<show object="true" label="true"/>
<objColor r="255" g="0" b="102" alpha="0.0" dynamicr="ca < 180°" dynamicg="0" dynamicb="ca > 180°" colorSpace="0"/>
<layer val="0"/>
<labelOffset x="-47" y="43"/>
<labelMode val="1"/>
<lineStyle thickness="6" 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="2.8959999999999986" A3="0.0" A4="-3.52" A5="-0.34"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="E"/>
</command>
<element type="point" label="E">
<show object="true" label="true"/>
<objColor r="51" g="51" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-25" y="14"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="0.4245461565011226" y="0.5078258107921081" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Line">
<input a0="E" a1="A"/>
<output a0="d_1"/>
</command>
<element type="line" label="d_1">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.16782581079210807" y="3.0954538434988774" z="-1.6432011607778387"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="c" a1="d_1"/>
<output a0="F_1" a1="F"/>
</command>
<element type="point" label="F_1">
<show object="false" label="true"/>
<objColor r="64" g="64" b="64" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.4245461565011226" y="0.5078258107921081" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="F">
<show object="true" label="true"/>
<objColor r="51" g="51" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="6.615453843498877" y="0.17217418920789185" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="E" a1="F"/>
<output a0="d"/>
</command>
<element type="segment" label="d">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-1" y="10"/>
<labelMode val="0"/>
<coords x="0.33565162158421624" y="6.190907686997755" z="-3.2864023215556775"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="C" a1="D"/>
<output a0="e"/>
</command>
<element type="segment" label="e">
<show object="true" label="false"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.5019095159125675" y="5.168745955538692" z="5.27049487359955"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
</construction>
</geogebra>