Relationship Between Central Angles, Arcs, and Chords
2024-12-27 02:25
This GeoGebra applet demonstrates the geometric relationships among central angles, arcs, and chords in a circle. Users can visually verify the theorem that equal central angles intercept equal arcs and equal chords. It includes ratio calculations and labels, helping learners understand their correspondence for plane geometry exploration.
In collections
Basic Properties of Circles
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SetValue(labelarc1, true)
ShowLabel(k, labelarc1)
SetValue(labelarc2, true)
ShowLabel(p, labelarc2)
SetValue(labelchord1, true)
ShowLabel(j, labelchord1)
SetValue(labelchord2, true)
ShowLabel(l, labelchord2)"/>
<caption val="比"/>
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<show object="false" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
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<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint x="8.281254668871593" y="3.0187453311284083" z="1"/>
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<expression label="ratio2" exp=""\frac{\overset{\LARGE{\frown}}{\small{AB}}}{\overset{\LARGE{\frown}}{\small{CD}}}=\frac{" + (LaTeX[k]) + "}{" + (LaTeX[p]) + "}=" + (LaTeX[FractionText[k / p]]) + """ />
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<show object="false" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint x="8.481254668871593" y="1.0187453311284083" z="1"/>
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<expression label="ratio3" exp=""\frac{AB}{CD}=\frac{" + (LaTeX[j]) + "}{" + (LaTeX[l]) + "}=" + (LaTeX[FractionText[round((100 * j)) / 100 / (round((100 * l)) / 100)]]) + """ />
<element type="text" label="ratio3">
<show object="false" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
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<expression label="text123" exp=""" + (LaTeX[ratio1]) + "\\\\" + (LaTeX[ratio2]) + "\\\\" + (LaTeX[ratio3]) + """ />
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<show object="true" label="true" ev="40"/>
<condition showObject="ratios ∧ o1 ∧ o2 ∧ o3"/>
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<isLaTeX val="true"/>
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<expression label="text12" exp=""" + (LaTeX[ratio1]) + "\\\\" + (LaTeX[ratio2]) + """ />
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<show object="true" label="true" ev="40"/>
<condition showObject="ratios ∧ o1 ∧ o2 ∧ (¬o3)"/>
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<condition showObject="ratios ∧ o1 ∧ (¬o2) ∧ o3"/>
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<font serif="true" sizeM="1" size="0" style="0"/>
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<show object="true" label="true" ev="8"/>
<condition showObject="ratios ∧ (¬o1) ∧ o2 ∧ o3"/>
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<isLaTeX val="true"/>
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</element>
<expression label="text1only" exp=""" + (LaTeX[ratio1]) + """ />
<element type="text" label="text1only">
<show object="true" label="true" ev="40"/>
<condition showObject="ratios ∧ o1 ∧ (¬o2) ∧ (¬o3)"/>
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<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
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</element>
<expression label="text2only" exp=""" + (LaTeX[ratio2]) + """ />
<element type="text" label="text2only">
<show object="true" label="true" ev="8"/>
<condition showObject="ratios ∧ (¬o1) ∧ o2 ∧ (¬o3)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
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<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
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</element>
<expression label="text3only" exp=""" + (LaTeX[ratio3]) + """ />
<element type="text" label="text3only">
<show object="true" label="true" ev="8"/>
<condition showObject="ratios ∧ (¬o1) ∧ (¬o2) ∧ o3"/>
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<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
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<element type="image" label="pic1">
<file name="46faf4dbc385f168a0cf0a9a5e23af7e/QSIP.png"/>
<inBackground val="false"/>
<absoluteScreenLocation x="6" y="467"/> <show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<selectionAllowed val="false"/>
</element>
</construction>
</geogebra>