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ASU 165 All Soviet Union MO 1972 perpendiculars inside a convex ABCD

Source:

July 3, 2019
geometryperpendicular

Problem Statement

Let OO be the intersection point of the diagonals of the convex quadrangle ABCDABCD . Prove that the line drawn through the points of intersection of the medians of triangles AOBAOB and CODCOD is orthogonal to the line drawn through the points of intersection of the heights of triangles BOCBOC and AODAOD .
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