Trigonometry & Inverse Trigonometry
Inscribed circles and successive triangles
Grade 11
Question:
<p><strong>Paragraph (Questions 7-8):</strong> Let the incircle of \(\triangle ABC\) touch sides \(BC, CA, AB\) at \(A_1, B_1, C_1\) respectively. The incircle of \(\triangle A_1B_1C_1\) touches its sides \(B_1C_1, C_1A_1, A_1B_1\) at \(A_2, B_2, C_2\) respectively and so on.</p><p>Find \(\lim_{n \to \infty} \angle A_n\)</p>
<p>(a) \(0\)</p>
<p>(b) \(\frac{\pi}{6}\)</p>
<p>(c) \(\frac{\pi}{4}\)</p>
<p>(d) \(\frac{\pi}{3}\)</p>
Step-by-Step Solution
Key Concept: When successive contact triangles are formed by inscribed circles, the angles converge to a fixed limit.
<p>Solution not provided in source text.</p>
Correct Answer: Unknown