MathDB
collinearity wanted, parallelograms given

Source: Balkan MO Shortlist 2013 G2 BMO

March 3, 2020
geometrycollinearparallelogramsparallelogram

Problem Statement

Let ABCDABCD be a quadrilateral, let OO be the intersection point of diagonals ACAC and BDBD, and let PP be the intersection point of sides ABAB and CDCD. Consider the parallelograms AODEAODE and BOCFBOCF. Prove that E,FE, F and PP are collinear.
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