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ASU 195 All Soviet Union MO 1974 right angle inside a square

Source:

July 4, 2019
perpendiculargeometrysquare

Problem Statement

Given a square ABCDABCD. Points PP and QQ are in the sides [AB][AB] and [BC][BC] respectively. ∣BP∣=∣BQ∣|BP|=|BQ|. Let HH be the foot of the perpendicular from the point BB to the segment [PC][PC]. Prove that the ∠DHQ=90o\angle DHQ =90^o .
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