Three congruent circles G₁, G₂, G₃ have a common point P.
Further, define
G₂ intersect G₃={A, P},
G₃ intersect G₁={B, P},
G₁ intersect G₂={C, P}.

(1) Prove that the point P is the orthocenter of triangle ABC.
(2) Prove that the circumcircle of triangle ABC is congruent to the given circles G₁, G₂, G₃.

(2) is not too hard once it is grasped that triangle ABC is congruent to triangle G1G2G3.

Since the triangles are congruent, so are their circumcircles.

Posted by broll on 2013-03-18 02:22:45