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.