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two circumcirlces given, perpendicularity wanted

Source: Finland 2014, Problem 2

September 1, 2019
geometrycircumcircleperpendicular

Problem Statement

The center of the circumcircle of the acute triangle ABCABC is MM, and the circumcircle of ABMABM meets BCBC and ACAC at PP and QQ (P≠BP\ne B). Show that the extension of the line segment CMCM is perpendicular to PQPQ.
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