Prove that a triangle is equilateral if and only if its centroid and circumcenter are the same point.

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- September 28th 2010, 02:13 PMMATNTRNGTriangle Centers Proof
Prove that a triangle is equilateral if and only if its centroid and circumcenter are the same point.

- September 28th 2010, 02:30 PMTraveller
One way is pretty easy. As for the other way, we assume that the centroid and circumcenter are the same point, say, G. Let D be the midpoint of BC. Since D and G are two common points of the median and perpendicular bisector corresponding to BC, they must be the same line. Can you complete the proof ?