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Source: Kyiv City MO 2023 Round 1, Problem 11.3

December 16, 2023
circumcirclegeometry

Problem Statement

Let II be the incenter of triangle ABCABC with AB<ACAB < AC. Point XX is chosen on the external bisector of ∠ABC\angle ABC such that IC=IXIC = IX. Let the tangent to the circumscribed circle of △BXC\triangle BXC at point XX intersect the line ABAB at point YY. Prove that AC=AYAC = AY.
Proposed by Oleksiy Masalitin
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