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.
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