MathDB
2013 BAMO12 p3 triangle with vertices circumcenters congruent to ABC

Source:

August 26, 2019
geometrycongruent trianglesCircumcenterorthocenter

Problem Statement

Let HH be the orthocenter of an acute triangle ABCABC. (The orthocenter is the point at the intersection of the three altitudes. An acute triangle has all angles less than 90o90^o.) Draw three circles: one passing through A,BA, B, and HH, another passing through B,CB, C, and HH, and finally, one passing through C,AC, A, and HH. Prove that the triangle whose vertices are the centers of those three circles is congruent to triangle ABCABC.