MathDB
Orthic triangle is isosceles

Source: Austrian Regional Competition for Advanced Students 2012, #4

May 23, 2012
trigonometrygeometry proposedgeometry

Problem Statement

In a triangle ABCABC, let HaH_a, HbH_b and HcH_c denote the base points of the altitudes on the sides BCBC, CACA and ABAB, respectively. Determine for which triangles ABCABC two of the lengths HaHbH_aH_b, HbHcH_bH_c and HaHcH_aH_c are equal.