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euler lines coincide, an yugoslavian beauty

Source: bmo 1990

April 23, 2007
Eulergeometryincenterprojective geometrygeometric transformationhomothetycircumcircle

Problem Statement

Let ABCABC be an acute triangle and let A1,B1,C1A_{1}, B_{1}, C_{1} be the feet of its altitudes. The incircle of the triangle A1B1C1A_{1}B_{1}C_{1} touches its sides at the points A2,B2,C2A_{2}, B_{2}, C_{2}. Prove that the Euler lines of triangles ABCABC and A2B2C2A_{2}B_{2}C_{2} coincide.
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