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6

Part of 1970 IMO Shortlist

Problems(1)

Prove that the circumcircles have a common point

Source:

9/23/2010
In the triangle ABCABC let B′B' and C′C' be the midpoints of the sides ACAC and ABAB respectively and HH the foot of the altitude passing through the vertex AA. Prove that the circumcircles of the triangles AB′C′AB'C',BC′HBC'H, and B′CHB'CH have a common point II and that the line HIHI passes through the midpoint of the segment B′C′.B'C'.
geometrycircumcircleEulerpower of a pointIMO Shortlist