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parallel wanted, cyclic convex pentagon given

Source: Austrian Regional Competition For Advanced Students 2019, p2

March 2, 2020
geometryCyclicparallelequal segments

Problem Statement

The convex pentagon ABCDEABCDE is cyclic and AB=BDAB = BD. Let point PP be the intersection of the diagonals ACAC and BEBE. Let the straight lines BCBC and DEDE intersect at point QQ. Prove that the straight line PQPQ is parallel to the diagonal ADAD.
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