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circumcenter equidistant from 2 points wanted, parallelogram related

Source: Czech-Polish-Slovak Junior Match 2014, Team p2 CPSJ

March 23, 2020
geometrycircumcircleparallelogramequal segments

Problem Statement

Let ABCDABCD be a parallelogram with ∠BAD<90o\angle BAD<90^o and AB>BCAB> BC . The angle bisector of BADBAD intersects line CDCD at point PP and line BCBC at point QQ. Prove that the center of the circle circumscirbed around the triangle CPQCPQ is equidistant from points BB and DD.
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