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B_1,A_1 touchpoints with incircle, K\in AB: AK = KB_1, BK = KA_1, show <C>=60

Source: St Petersburg Olympiad 2016, Grade 10, P3

September 8, 2018
geometryincircleangle bisector

Problem Statement

The circle inscribed in the triangle ABCABC is tangent to side ACAC at point B1B_1, and to side BCBC at point A1A_1. On the side ABAB there is a point KK such that AK=KB1,BK=KA1AK = KB_1, BK = KA_1. Prove that ∠ACB≥60 \angle ACB\ge 60
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