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orthocenter collinear with intersections of circles of diameter BN,CM

Source: Switzerland - Swiss MO 2005 p8

July 19, 2020
geometryorthocentercollinearcircles

Problem Statement

Let ABCABC be an acute-angled triangle. M,NM ,N are any two points on the sides AB,ACAB , AC respectively. The circles with the diameters BNBN and CMCM intersect at points PP and QQ. Show that the points P,QP, Q and the orthocenter of the triangle ABCABC lie on a straight line.
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