IMO 1971 LL GDR20

Let M be the circumcenter of a triangle ABC. The line through

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IMO 1971 LL GDR20

Origin: GDR

Problem

Let M be the circumcenter of a triangle ABC. The line through M perpendicular to CM meets the lines CA and CB at Q and P respec- tively. Prove that CP CM CQ CM AB PQ = 2.