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IMO ShortList 2002, geometry problem 7

Source: IMO ShortList 2002, geometry problem 7

September 28, 2004
geometryincenterIMO ShortlistIran Lemmaradical axisPolarsgeometry solved

Problem Statement

The incircle Ω \Omega of the acute-angled triangle ABC ABC is tangent to its side BC BC at a point K K. Let AD AD be an altitude of triangle ABC ABC, and let M M be the midpoint of the segment AD AD. If N N is the common point of the circle Ω \Omega and the line KM KM (distinct from K K), then prove that the incircle Ω \Omega and the circumcircle of triangle BCN BCN are tangent to each other at the point N N.
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