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.