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2008 JBMO Shortlist G9

Source: 2008 JBMO Shortlist G9

October 10, 2017
JBMOgeometry

Problem Statement

Let OO be a point inside the parallelogram ABCDABCD such that ∠AOB+∠COD=∠BOC+∠AOD\angle AOB + \angle COD = \angle BOC + \angle AOD. Prove that there exists a circle kk tangent to the circumscribed circles of the triangles △AOB,△BOC,△COD\vartriangle AOB, \vartriangle BOC, \vartriangle COD and △DOA\vartriangle DOA.
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