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Congruent Triangles

Source: ToT - 2001 Spring Senior A-Level #3

August 17, 2011
geometryparallelogramgeometry 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 △AHBHC\triangle AH_BH_C, △BHAHC\triangle BH_AH_C and △CHAHB\triangle CH_AH_B is congruent to △HAHBHC\triangle H_AH_BH_C.
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