Let Γ be the circumcircle of triangle ABC. A circle Ω is tangent to the line segment AB and is tangent to Γ at a point lying on the same side of the line AB as C. The angle bisector of ∠BCA intersects Ω at two different points P and Q.
Prove that ∠ABP=∠QBC. geometryTriangleanglesEGMOEGMO 2018geometry solvedpower of a point