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angle chasing, angle bisectors (V Soros Olympiad 1998-99 Round 1 10.6)

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May 25, 2024
geometryangle bisectorangles

Problem Statement

In triangle ABCABC, the bisectors of the internal angles AA1AA_1 , BB1BB_1 and CC1CC_1 are drawn (A1,B1A_1, B_1, C1C_1 - on the sides of the triangle). It is known that ∠AA1C=∠AC1B1\angle AA_1C = \angle AC_1B_1. Find ∠BCA\angle BCA.
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