Let ABC be an acute triangle. Suppose that circle Γ1 has it's center on the side AC and is tangent to the sides AB and BC, and circle Γ2 has it's center on the side AB and is tangent to the sides AC and BC. The circles Γ1 and Γ2 intersect at two points P and Q. Show that if A,P,Q are collinear, then AB=AC. geometrycirclescollineartangent