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Triangle Proof

Source: ToT - 2001 Spring Junior A-Level #6

August 17, 2011
geometrygeometry unsolved

Problem Statement

Let AHAAH_A, BHBBH_B and CHCCH_C be the altitudes of triangle △ABC\triangle ABC. Prove that the triangle whose vertices are the intersection points of the altitudes of triangles △AHBHC\triangle AH_BH_C, △BHAHC\triangle BH_AH_C and △CHAHB\triangle CH_AH_B is equal to triangle △HAHBHC\triangle H_AH_BH_C.
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