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52 lines
2.3 KiB
HTML
52 lines
2.3 KiB
HTML
<div class="book-prose">
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<h2 id="history" class="book-prose__heading">History</h2>
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<p>
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Circle theorems were developed in classical geometry and refined through Euclidean proofs. They
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remain central in modern school geometry due to their structured reasoning style.
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</p>
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<h2 id="checkpoints" class="book-prose__heading">Checkpoints</h2>
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<details class="book-question">
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<summary class="book-question__prompt">If central angle is \(100^\circ\), what is inscribed angle on same arc?</summary>
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<div class="book-question__solution">
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<p><strong>Answer:</strong> \(50^\circ\).</p>
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</div>
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</details>
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<details class="book-question">
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<summary class="book-question__prompt">In a cyclic quadrilateral, one angle is \(72^\circ\). Find opposite angle.</summary>
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<div class="book-question__solution">
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<p><strong>Answer:</strong> \(108^\circ\).</p>
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</div>
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</details>
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<details class="book-question">
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<summary class="book-question__prompt">What angle is formed by radius and tangent at point of contact?</summary>
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<div class="book-question__solution">
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<p><strong>Answer:</strong> \(90^\circ\).</p>
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</div>
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</details>
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<details class="book-question">
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<summary class="book-question__prompt">Two tangents from external point \(P\) touch at \(A,B\). Compare \(PA\) and \(PB\).</summary>
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<div class="book-question__solution">
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<p><strong>Answer:</strong> \(PA=PB\).</p>
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</div>
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</details>
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<details class="book-question">
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<summary class="book-question__prompt">Why does one theorem name per step improve proof quality?</summary>
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<div class="book-question__solution">
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<p><strong>Answer:</strong> It makes logical justification explicit and verifiable.</p>
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</div>
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</details>
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<h2 id="applications" class="book-prose__heading">Applications</h2>
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<ul>
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<li><strong>Design:</strong> arcs and tangency in mechanical/architectural drawings.</li>
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<li><strong>Optics:</strong> circular geometry in lenses and reflective paths.</li>
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<li><strong>CAD tools:</strong> tangent/chord constraints in modeling software.</li>
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</ul>
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<h2 id="references" class="book-prose__heading">References</h2>
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<ul>
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<li>Standard high-school geometry materials on circle theorems.</li>
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<li>Classical Euclidean geometry references.</li>
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</ul>
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</div>
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