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sides AB,CD of cyclic ABCD are parallel or the diagonals are perpendicular

Source: 1982 Polish MO Finals p2

February 25, 2020
Cyclicparallelperpendicular

Problem Statement

In a cyclic quadrilateral ABCDABCD the line passing through the midpoint of ABAB and the intersection point of the diagonals is perpendicular to CDCD. Prove that either the sides ABAB and CDCD are parallel or the diagonals are perpendicular.
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