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<AQC =< PQB, <DRQ = 45^o, right isosceles (2004 Romania District VII P4)

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May 24, 2020
geometryanglesequal anglesisoscelesright triangle

Problem Statement

Consider the isosceles right triangle ABCABC (AB=ACAB = AC) and the points M,P∈[AB]M, P \in [AB] so that AM=BPAM = BP. Let DD be the midpoint of the side BCBC and R,QR, Q the intersections of the perpendicular from AA onCM CM with CMCM and BCBC respectively. Prove that
a) ∠AQC=∠PQB\angle AQC = \angle PQB b) ∠DRQ=45o\angle DRQ = 45^o
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