圆的基本概念
2013-03-21 03:18
本 GeoGebra 范例演示了圆的基本概念与几何构造。通过点、线段、圆弧和直线等基础几何元素的交互,直观展示了圆心、半径、圆弧、弦以及直线与圆的交点等核心属性。该模型有助于学生深入理解平面几何中圆的定义及其相关几何特征,是学习基础几何作图的优质素材。
<?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>