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tangent of incircle, angle bisector and side of isosceles concurrent

Source: - All-Russian MO 2003 Regional (R4) 9.3

September 17, 2024
geometryincircleconcurrencyconcurrentisosceles

Problem Statement

In an isosceles triangle ABCABC (AB=BCAB = BC), the midline parallel to side BCBC intersects the incircle at a point FF that does not lie on the base ACAC. Prove that the tangent to the circle at point FF intersects the bisector of angle CC on side ABAB.