Geometric Construction Problem: Circles, Polygons, and Circular Sectors
2019-04-23 02:47
This GeoGebra example presents a comprehensive geometric construction problem demonstrating the use of fundamental commands including Circle, Point, Polygon, Segment, CircleSector, and CircleArc. The construction features multiple key points (A, B, C, D, E), various circle and arc objects, and text annotations, potentially involving concepts such as geometric mean, complex numbers, or functions. T
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<gui>
<window width="825" height="464" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.4" orientation="1" />
</panes>
<views>
<view id="1" visible="true" inframe="false" stylebar="false" location="1" size="500" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="200" window="100,100,250,400" />
<view id="4" visible="false" inframe="false" stylebar="false" location="1,1" size="300" window="100,100,600,400" />
<view id="8" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="4097" visible="false" inframe="false" stylebar="true" location="1,1,1,1" size="400" window="100,100,700,550" />
<view id="512" visible="false" inframe="false" stylebar="false" location="1,1,1" size="500" window="100,100,600,400" />
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<toolbar show="false" 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="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="24"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="822" height="459"/>
<coordSystem xZero="46.1999999999998" yZero="376.9999999999999" scale="54.999999999999964" yscale="55.00000000000001"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="1" rightAngleStyle="1" checkboxSize="26" 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="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<grid distX="1" distY="1" distTheta="0.5235987755982988"/>
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<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="point" label="A">
<show object="false" label="true"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="0" y="2" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="B">
<show object="false" label="true"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="3" y="2" z="1"/>
<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="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-5" A3="0" A4="0" A5="-2"/>
<eqnStyle style="specific"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-3" y="2.0000000000000004" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="1.8369701987210297e-16" y="-1" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="numeric" label="t">
<value val="0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="1" absoluteScreenLocation="true" width="200" x="516" y="221" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.05" speed="5" type="3" playing="false"/>
</element>
<expression label="text1" exp=""計算下圖著色部分的面積。""/>
<element type="text" label="text1">
<show object="true" label="false" ev="40"/>
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<fixed val="true"/>
<absoluteScreenLocation x="21" y="38"/>
</element>
<element type="boolean" label="a">
<value val="false"/>
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<labelOffset x="348" y="10"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[t, 0]
StartAnimation[t, a]"/>
<caption val="提示"/>
</element>
<command name="Polygon">
<input a0="{A, A + (3, 0), A + (3, 3), A + (0, 3)}"/>
<output a0="q1"/>
</command>
<element type="polygon" label="q1">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.30000001192092896"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<expression label="E" exp="A + (t * (8, 0))" type="point" />
<element type="point" label="E">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="2" z="1"/>
<pointSize val="4"/>
<pointStyle val="1"/>
</element>
<expression label="text2" exp=""−""/>
<element type="text" label="text2">
<show object="true" label="false" ev="40"/>
<condition showObject="t ≟ 1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="false" sizeM="2" size="24" style="0"/>
<startPoint x="3.640000000000011" y="3.239999999999993" z="1"/>
</element>
<command name="Segment">
<input a0="E" a1="E + (3, 0)"/>
<output a0="f"/>
</command>
<element type="segment" label="f">
<show object="true" label="true" ev="4"/>
<condition showObject="t > 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-33" y="12"/>
<labelMode val="3"/>
<coords x="0" y="3" z="-6"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
<caption val="16 cm"/>
</element>
<command name="CircleSector">
<input a0="E" a1="E + (3, 0)" a2="E + (0, 3)"/>
<output a0="d"/>
</command>
<element type="conicpart" label="d">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="255" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-5" A3="0" A4="0" A5="-2"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="CircleSector">
<input a0="E" a1="E + (3, 0)" a2="E + (0, 3)"/>
<output a0="e"/>
</command>
<element type="conicpart" label="e">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-5" A3="0" A4="0" A5="-2"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="A" a1="B"/>
<output a0="g"/>
</command>
<element type="segment" label="g">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
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<coords x="0" y="3" z="-6"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
<caption val="16 cm"/>
</element>
<command name="CircleArc">
<input a0="E" a1="E + (0, 3)" a2="E + (3, 0)"/>
<output a0="h"/>
</command>
<element type="conicpart" label="h">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 1"/>
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<lineStyle thickness="5" type="10" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-5" A3="0" A4="0" A5="-2"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="E" a1="E - (3, 0)"/>
<output a0="i"/>
</command>
<element type="segment" label="i">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="-3" z="6"/>
<lineStyle thickness="5" type="10" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="E" a1="E - (0, 3)"/>
<output a0="j"/>
</command>
<element type="segment" label="j">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
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<lineStyle thickness="5" type="10" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
</construction>
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