MathDB

9.3

Part of 2003 All-Russian Olympiad Regional Round

Problems(1)

tangent of incircle, angle bisector and side of isosceles concurrent

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

9/17/2024
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.
geometryincircleconcurrencyconcurrentisosceles