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Angles in a Quadrilateral

Source: Singapore Junior Math Olympiad 2023 2nd Round

July 27, 2023
geometry

Problem Statement

In a convex quadrilateral ABCDABCD, the diagonals intersect at OO, and MM and NN are points on the segments OAOA and ODOD respectively. Suppose MNMN is parallel to ADAD and NCNC is parallel to ABAB. Prove that ∠ABM=∠NCD\angle ABM=\angle NCD.
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