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AP _|_BQ if AQ_|_DP, AB = AD, <B = < D = 90 ^o

Source: Mathematics Regional Olympiad of Mexico Center Zone 2008 P6

November 9, 2021
geometryperpendicular

Problem Statement

In the quadrilateral ABCDABCD, we have AB=ADAB = AD and ∠B=∠D=90∘\angle B = \angle D = 90 ^ \circ . The points PP and QQ lie on BCBC and CDCD, respectively, so that AQAQ is perpendicular on DPDP. Prove that APAP is perpendicular to BQBQ.
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