If the incener of a triangle is also is circumcenter, what type of triangle is it?

Answer 1

The incenter is the point where the 3 angle bisectors meet. It is the center of an inscribed (inner) circle.

The circumcenter is the point where the 3 perpendicular side bisectors meet. It is the center of a circumscribed (outer) circle.

If the are the same point, then you must have all sides and all angles equal in the triangle.

This is an equilateral triangle.