The perpendicular bisector and the angle bisector of an equilateral triangle are the same and they pass through the circumcentre.
In an equilateral triangle a perpendicular bisector of a side will also be the angular bisector for the opposite angle.
∵ The perpendicular bisector of chord of a circle passes through the centre of the circle
∵ Perpendicular bisectors of an equilateral triangle passes through the centre of the circle.