Demonstration of Positional Relationships among Points, Lines, and Circles

2020-10-15 00:06

This GeoGebra applet intuitively demonstrates the positional relationships between points and circles, as well as lines and circles. By constructing circles, points, lines, and segments, and utilizing intersection commands, it dynamically displays the position of a point relative to a circle and the states of a line intersecting, tangent to, or disjoint from a circle. This material is suitable for

#circle #geometry-construction #coordinate-geometry

<?xml version="1.0" encoding="utf-8"?>
<geogebra format="4.0" id="c8b69315-af11-41f3-88f0-7b8949fb3ac0"  xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
	<window width="875" height="713" />
	<perspectives>
<perspective id="tmp">
	<panes>
		<pane location="" divider="0.25142857142857145" 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="300" window="100,100,600,400" />
		<view id="1" visible="true" inframe="false" stylebar="false" location="1" size="643" window="100,100,600,400" />
		<view id="2" visible="true" inframe="false" stylebar="false" location="3" size="220" window="100,100,250,400" />
		<view id="16" visible="false" inframe="true" stylebar="false" location="1" size="150" window="50,50,500,500" />
		<view id="32" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
		<view id="64" visible="false" inframe="true" stylebar="false" 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 , 14 66 68 | 25 52 60 61 || 40 41 42 , 27 28 35 , 6" />
	<input show="true" cmd="true" top="false" />
</perspective>
	</perspectives>
	<labelingStyle  val="3"/>
	<font  size="16"/>
	<graphicsSettings javaLatexFonts="false"/>
	<consProtColumns  col0="true" col1="true" col2="false" col3="true" col4="false" col5="true" col6="true" col7="false"/>
	<consProtocol useColors="true" addIcons="false" showOnlyBreakpoints="false"/>
</gui>
<euclidianView>
	<size  width="643" height="556"/>
	<coordSystem xZero="215.0000000000001" yZero="315.00000000000006" scale="50.00000000000003" yscale="50.00000000000003"/>
	<evSettings axes="true" grid="true" 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="204" g="204" b="204"/>
	<lineStyle axes="1" grid="10"/>
	<axis id="0" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
	<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<kernel>
	<continuous val="false"/>
	<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="">
<command name="Intersect">
	<input a0="xAxis" a1="yAxis"/>
	<output a0="O"/>
</command>
<element type="point" label="O">
	<show object="true" label="true"/>
	<objColor r="255" g="51" b="51" alpha="0.0"/>
	<layer val="0"/>
	<labelOffset x="-28" y="27"/>
	<labelMode val="0"/>
	<coords x="0.0" y="-0.0" z="1.0"/>
	<pointSize val="3"/>
	<pointStyle val="0"/>
</element>
<command name="Point">
	<input a0="xAxis"/>
	<output a0="B"/>
</command>
<element type="point" label="B">
	<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"/>
	<coords x="3.0" y="0.0" z="1.0"/>
	<pointSize val="3"/>
	<pointStyle val="0"/>
</element>
<command name="Circle">
	<input a0="O" a1="B"/>
	<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="-9.0" A3="0.0" A4="-0.0" A5="0.0"/>
	<eqnStyle style="specific"/>
</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="7.44" y="-0.4" z="1.0"/>
	<pointSize val="3"/>
	<pointStyle val="0"/>
</element>
<element type="point" label="D">
	<show object="false" 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="6.62" y="5.32" z="1.0"/>
	<pointSize val="3"/>
	<pointStyle val="0"/>
</element>
<element type="point" label="E">
	<show object="false" 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="5.7" y="6.04" z="1.0"/>
	<pointSize val="3"/>
	<pointStyle val="0"/>
</element>
<command name="Segment">
	<input a0="D" a1="E"/>
	<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="-0.7199999999999998" y="-0.9199999999999999" z="9.660799999999998"/>
	<lineStyle thickness="2" type="0" typeHidden="1"/>
	<eqnStyle style="implicit"/>
	<outlyingIntersections val="false"/>
	<keepTypeOnTransform val="true"/>
</element>
<command name="Line">
	<input a0="C" a1="a"/>
	<output a0="b"/>
</command>
<element type="line" label="b">
	<show object="true" label="false"/>
	<objColor r="0" g="0" b="0" alpha="0.0"/>
	<layer val="0"/>
	<labelMode val="0"/>
	<coords x="-0.7199999999999998" y="-0.9199999999999999" z="4.988799999999998"/>
	<lineStyle thickness="2" type="0" typeHidden="1"/>
	<eqnStyle style="implicit"/>
</element>
<element type="point" label="P">
	<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="1" playing="false"/>
	<coords x="3.0" y="2.0" z="1.0"/>
	<pointSize val="3"/>
	<pointStyle val="0"/>
</element>
<expression label="text1" exp="&quot;移動C，觀察與圓心的距離&#10;移動P，觀察與圓心的距離&quot;"/>
<element type="text" label="text1">
	<show object="true" label="false"/>
	<objColor r="0" g="153" b="51" alpha="0.0"/>
	<layer val="0"/>
	<labelMode val="0"/>
	<startPoint  x="4.7999999999999945" y="5.539999999999997" z="1.0"/>
</element>
</construction>
</geogebra>

<?xml version="1.0" encoding="utf-8"?>
<geogebra format="4.0" id="c8b69315-af11-41f3-88f0-7b8949fb3ac0"  xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
	<window width="875" height="713" />
	<perspectives>
<perspective id="tmp">
	<panes>
		<pane location="" divider="0.25142857142857145" 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="300" window="100,100,600,400" />
		<view id="1" visible="true" inframe="false" stylebar="false" location="1" size="643" window="100,100,600,400" />
		<view id="2" visible="true" inframe="false" stylebar="false" location="3" size="220" window="100,100,250,400" />
		<view id="16" visible="false" inframe="true" stylebar="false" location="1" size="150" window="50,50,500,500" />
		<view id="32" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
		<view id="64" visible="false" inframe="true" stylebar="false" 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 , 14 66 68 | 25 52 60 61 || 40 41 42 , 27 28 35 , 6" />
	<input show="true" cmd="true" top="false" />
</perspective>
	</perspectives>
	<labelingStyle  val="3"/>
	<font  size="16"/>
	<graphicsSettings javaLatexFonts="false"/>
	<consProtColumns  col0="true" col1="true" col2="false" col3="true" col4="false" col5="true" col6="true" col7="false"/>
	<consProtocol useColors="true" addIcons="false" showOnlyBreakpoints="false"/>
</gui>
<euclidianView>
	<size  width="643" height="556"/>
	<coordSystem xZero="215.0000000000001" yZero="315.00000000000006" scale="50.00000000000003" yscale="50.00000000000003"/>
	<evSettings axes="true" grid="true" 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="204" g="204" b="204"/>
	<lineStyle axes="1" grid="10"/>
	<axis id="0" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
	<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<kernel>
	<continuous val="false"/>
	<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="">
<command name="Intersect">
	<input a0="xAxis" a1="yAxis"/>
	<output a0="O"/>
</command>
<element type="point" label="O">
	<show object="true" label="true"/>
	<objColor r="255" g="51" b="51" alpha="0.0"/>
	<layer val="0"/>
	<labelOffset x="-28" y="27"/>
	<labelMode val="0"/>
	<coords x="0.0" y="-0.0" z="1.0"/>
	<pointSize val="3"/>
	<pointStyle val="0"/>
</element>
<command name="Point">
	<input a0="xAxis"/>
	<output a0="B"/>
</command>
<element type="point" label="B">
	<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"/>
	<coords x="3.0" y="0.0" z="1.0"/>
	<pointSize val="3"/>
	<pointStyle val="0"/>
</element>
<command name="Circle">
	<input a0="O" a1="B"/>
	<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="-9.0" A3="0.0" A4="-0.0" A5="0.0"/>
	<eqnStyle style="specific"/>
</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="7.44" y="-0.4" z="1.0"/>
	<pointSize val="3"/>
	<pointStyle val="0"/>
</element>
<element type="point" label="D">
	<show object="false" 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="6.62" y="5.32" z="1.0"/>
	<pointSize val="3"/>
	<pointStyle val="0"/>
</element>
<element type="point" label="E">
	<show object="false" 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="5.7" y="6.04" z="1.0"/>
	<pointSize val="3"/>
	<pointStyle val="0"/>
</element>
<command name="Segment">
	<input a0="D" a1="E"/>
	<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="-0.7199999999999998" y="-0.9199999999999999" z="9.660799999999998"/>
	<lineStyle thickness="2" type="0" typeHidden="1"/>
	<eqnStyle style="implicit"/>
	<outlyingIntersections val="false"/>
	<keepTypeOnTransform val="true"/>
</element>
<command name="Line">
	<input a0="C" a1="a"/>
	<output a0="b"/>
</command>
<element type="line" label="b">
	<show object="true" label="false"/>
	<objColor r="0" g="0" b="0" alpha="0.0"/>
	<layer val="0"/>
	<labelMode val="0"/>
	<coords x="-0.7199999999999998" y="-0.9199999999999999" z="4.988799999999998"/>
	<lineStyle thickness="2" type="0" typeHidden="1"/>
	<eqnStyle style="implicit"/>
</element>
<element type="point" label="P">
	<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="1" playing="false"/>
	<coords x="3.0" y="2.0" z="1.0"/>
	<pointSize val="3"/>
	<pointStyle val="0"/>
</element>
<expression label="text1" exp="&quot;移動C，觀察與圓心的距離&#10;移動P，觀察與圓心的距離&quot;"/>
<element type="text" label="text1">
	<show object="true" label="false"/>
	<objColor r="0" g="153" b="51" alpha="0.0"/>
	<layer val="0"/>
	<labelMode val="0"/>
	<startPoint  x="4.7999999999999945" y="5.539999999999997" z="1.0"/>
</element>
</construction>
</geogebra>