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Concurrent on the Euler line

Source: Gazeta Matematica - Romania TST 2011- Second exam - P2

March 5, 2012
Eulergeometrysearchcircumcircleincentergeometric transformationhomothety

Problem Statement

In triangle ABCABC, the incircle touches sides BC,CABC,CA and ABAB in D,ED,E and FF respectively. Let XX be the feet of the altitude of the vertex DD on side EFEF of triangle DEFDEF. Prove that AX,BYAX,BY and CZCZ are concurrent on the Euler line of the triangle DEFDEF.
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