Proving equilaterial triangle using centroid and circumcenter
I am asked to: Prove that a triangle is equilaterial if and only if its centroid and circumcenter coincide.
I know that:
(a) centroid of a triangle is the point where the three medians (a segment joining a vertex of a triangle to the midpoint of the opposite side) of the triangle intersect.
(b) circumcenter of a triangle is the point where the three pependicular bisectors (a line segment that is both perpendicular to a side of a triangle and passes through its midpoint) of a triangle intersect.
But I don't know how to do the proof or what definitions/theorems are used for the proof.