Let Γ1 and Γ2 be two circles intersecting at P and Q. The common tangent, closer to P, of Γ1 and Γ2 touches Γ1 at A and Γ2 at B. The tangent of Γ1 at P meets Γ2 at C, which is different from P, and the extension of AP meets BC at R.
Prove that the circumcircle of triangle PQR is tangent to BP and BR. geometrycircumcirclegeometric transformation