MathDB

9

Part of 2011 Ukraine Team Selection Test

Problems(1)

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

Source: Ukraine TST 2011 p9

5/5/2020
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 .
geometrycircumcircleequal anglestangent circlesTangentscyclic quadrilateral