_{1}, G

_{2}, G

_{3}have a common point P.

Further, define

G

_{2}intersect G

_{3}={A, P},

G

_{3}intersect G

_{1}={B, P},

G

_{1}intersect G

_{2}={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 G_{1}, G_{2}, G_{3}.