IMO Shortlist 1970 problem 6


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2. travnja 2012.
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In the triangle ABC let B' and C' be the midpoints of the sides AC and AB respectively and H the foot of the altitude passing through the vertex A. Prove that the circumcircles of the triangles AB'C',BC'H, and B'CH have a common point I and that the line HI passes through the midpoint of the segment B'C'.
Izvor: Međunarodna matematička olimpijada, shortlist 1970