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Four Coin Theorem (Posted on 2013-03-17) Difficulty: 3 of 5
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.

No Solution Yet Submitted by Danish Ahmed Khan    
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Some Thoughts 2 only | Comment 1 of 2

(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
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