IMO 2011 Shortlist G1

Let ABC be an acute triangle. Let ω be a circle whose center L lies on the side BC. Suppose that ω is tangent to AB at B...

IMO 2011 Shortlist G1

Category: Geometry

Problem

Let ABC be an acute triangle. Let ω be a circle whose center L lies on the side BC. Suppose that ω is tangent to AB at B′ and to AC at C′ . Suppose also that the circumcenter O of the triangle ABC lies on the shorter arc B′ C′ of ω. Prove that the circumcircle of ABC and ω meet at two points.