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Math Help - Triangle Centers Proof

  1. #1
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    Triangle Centers Proof

    Prove that a triangle is equilateral if and only if its centroid and circumcenter are the same point.
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  2. #2
    Member Traveller's Avatar
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    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 ?
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