Draw incircle of

Steps of Construction:

1. Draw an equilateral triangle of side 4.6cm

2. Draw angle bisector of ∠A.

3. Draw angle bisector of ∠B.

4. They intersect each other at P.

5. From P, drop a perpendicular on the line AB.

6. With P as center and length of perpendicular as the radius, draw a circle.

This circle is the incircle for the equilateral triangle.

Yes. The incenter and circumcenter of the equilateral triangle coincide with each other. This is because the perpendicular dropped from P on AP is also the perpendicular bisector of AB.