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Prove angle relation given parallelogram

Source: CSEMO 2018 Grade 11 Q3

July 30, 2018
geometryparallelogram

Problem Statement

Let OO be the circumcenter of △ABC\triangle ABC, where ∠ABC>90∘\angle ABC> 90^{\circ} and MM is the midpoint of BCBC. Point PP lies inside △ABC\triangle ABC such that PB⊥PCPB\perp PC. D,ED,E distinct from PP lies on the perpendicular to APAP through PP such that BD=BP,CE=CPBD=BP, CE=CP. If quadrilateral ADOEADOE is a parallelogram, prove that ∠OPE=∠AMB.\angle OPE = \angle AMB.
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