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midpoint wanted, right angles inside a rectagle (Kharkiv City XI 2015 - Ukr)

Source:

March 15, 2020
geometryrectangleKharkivright anglemidpoint

Problem Statement

In the rectangle ABCDABCD, point MM is the midpoint of the side BCBC. The points PP and QQ lie on the diagonal ACAC such that ∠DPC=∠DQM=90o\angle DPC = \angle DQM = 90^o. Prove that QQ is the midpoint of the segment APAP.
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