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Configuration with a paralellogram

Source: IMOC 2023 G1

September 9, 2023
geometryparallelogram

Problem Statement

Triangle ABCABC has circumcenter OO. MM is the midpoint of arc BCBC not containing AA. SS is a point on (ABC)(ABC) such that ASAS and BCBC intersect on the line passing through OO and perpendicular to AMAM. DD is a point such that ABDCABDC is a parallelogram. Prove that DD lies on the line SMSM.
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