MathDB
IMO Shortlist 2010 - Problem G5

Source:

July 17, 2011
geometrycircumcirclereflectionparallelogramIMO Shortlist

Problem Statement

Let ABCDEABCDE be a convex pentagon such that BC∥AE,BC \parallel AE, AB=BC+AE,AB = BC + AE, and ∠ABC=∠CDE.\angle ABC = \angle CDE. Let MM be the midpoint of CE,CE, and let OO be the circumcenter of triangle BCD.BCD. Given that ∠DMO=90∘,\angle DMO = 90^{\circ}, prove that 2∠BDA=∠CDE.2 \angle BDA = \angle CDE.
Proposed by Nazar Serdyuk, Ukraine
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