Problem

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Tags: geometry, circumcircle, parallelogram



Let ABCD be an inscribed quadrilateral in a circumference with center O such that it lies inside ABCD and BAC=ODA. Let E be the intersection of AC with BD. Lines r and s are drawn through E such that r is perpendicular to BC, and s is perpendicular to AD. Let P be the intersection of r with AD, and M the intersection of s with BC. Let N be the midpoint of EO. Prove that M, N, and P lie on a line.