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Convex Pentagon

Source: Nepal Mathematics Olympiad

April 22, 2018
geometry

Problem Statement

Problem Section #3
c) Let ABCDEABCDE be a convex pentagon such that BC∥AE,AB=BC+AEBC \parallel AE, AB = BC + AE, and ∠ABC=∠CDE\angle{ABC} =\angle{CDE}. Let MM be the midpoint of CECE, and let OO be the circumcenter of triangle BCDBCD. Given that ∠DMO=90o\angle{DMO}=90^{o}, prove that 2∠BDA=∠CDE2\angle{BDA} =\angle{CDE}.
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