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Show that CM is perpendicular to PQ with circumcenter M

Source: Turkey IMO TST 1993 #2

July 7, 2011
geometrycircumcirclegeometry unsolved

Problem Statement

Let MM be the circumcenter of an acute-angled triangle ABCABC. The circumcircle of triangle BMABMA intersects BCBC at PP and ACAC at QQ. Show that CM⊥PQCM \perp PQ.
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