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circle tangent to 2 lines and 2 circumcircles, cyclic, <PBC = <PDA, <PCB =<PAD

Source: Ukraine TST 2011 p9

May 5, 2020
geometrycircumcircleequal anglestangent circlesTangentscyclic quadrilateral

Problem Statement

Inside the inscribed quadrilateral ABCD ABCD , a point P P is marked such that ∠PBC=∠PDA \angle PBC = \angle PDA , ∠PCB=∠PAD \angle PCB = \angle PAD . Prove that there exists a circle that touches the straight lines AB AB and CD CD , as well as the circles circumscribed by the triangles ABP ABP and CDP CDP .
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