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BQ = 2QC, CR = 2RA, < PRQ = 90^o , equal angles wanted

Source: Olimpíada de Mayo / Maio (May Olympiad) 2019 L2

July 11, 2019
geometryequal angles

Problem Statement

On the sides AB,BCAB, BC and CACA of a triangle ABCABC are located the points P,QP, Q and RR respectively, such that BQ=2QC,CR=2RABQ = 2QC, CR = 2RA and ∠PRQ=90o\angle PRQ = 90^o. Show that ∠APR=∠RPQ\angle APR =\angle RPQ.
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