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Part of 2021 Lotfi Zadeh Olympiad

Problems(1)

Cyclic quadrilateral given. Parallelity wanted

Source: Lotfi Zadeh Olympiad 2021, Problem 1

12/28/2021
In the inscribed quadrilateral ABCDABCD, PP is the intersection point of diagonals and MM is the midpoint of arc ABAB. Prove that line MPMP passes through the midpoint of segment CDCD, if and only if lines AB,CDAB, CD are parallel.
geometryParallel Linescyclic quadrilateralLotfi Zadeh MO