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Two touching circles

Source: Indonesian National Science Olympiad 2018, Mathematics P2

July 6, 2018
geometry

Problem Statement

Let Γ1,Γ2\Gamma_1, \Gamma_2 be circles that touch at a point AA, and Γ2\Gamma_2 is inside Γ1\Gamma_1. Let BB be on Γ2\Gamma_2, and let ABAB intersect Γ1\Gamma_1 on CC. Let DD be on Γ1\Gamma_1 and PP be on the line CDCD (may be outside of the segment CDCD). BPBP intersects Γ2\Gamma_2 at QQ. Prove that A,D,P,QA,D,P,Q lie on a circle.
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