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equal angles related to a trapezoid

Source: Ukrainian Geometry Olympiad 2017, IX p2

December 11, 2018
geometrytrapezoidequal anglesAngle Chasing

Problem Statement

Point MM is the midpoint of the base BCBC of trapezoid ABCDABCD. On base ADAD, point PP is selected. Line PMPM intersects line DCDC at point QQ, and the perpendicular from PP on the bases intersects line BQBQ at point KK. Prove that ∠QBC=∠KDA\angle QBC = \angle KDA.
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