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ABCD Parallelogram with circle tangent to AB

Source: Turkey Junior National Olympiad 2022 P4

December 23, 2022
geometrycircumcircle

Problem Statement

In parallellogram ABCDABCD, on the arc BCBC of the circumcircle (ABC)(ABC), not containing the point AA, we take a point PP and on the [AC[AC, we take a point QQ such that ∠PBC=∠CDQ\angle PBC= \angle CDQ. Prove that (APQ)(APQ) is tangent to ABAB.
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