2013 BAMO12 p3 triangle with vertices circumcenters congruent to ABC
Source:
August 26, 2019
geometrycongruent trianglesCircumcenterorthocenter
Problem Statement
Let be the orthocenter of an acute triangle . (The orthocenter is the point at the intersection of the three altitudes. An acute triangle has all angles less than .) Draw three circles: one passing through , and , another passing through , and , and finally, one passing through , and . Prove that the triangle whose vertices are the centers of those three circles is congruent to triangle .