IMO Shortlist 2002 problem G7
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Avg: 9,0 The incircle of the acute-angled triangle is tangent to its side at a point . Let be an altitude of triangle , and let be the midpoint of the segment . If is the common point of the circle and the line (distinct from ), then prove that the incircle and the circumcircle of triangle are tangent to each other at the point .
Izvor: Međunarodna matematička olimpijada, shortlist 2002