Does a triangle always have a point where each side subtends equal 120° angles?

Question

Is there a point $O$ inside a triangle $\ riangle ABC$ (any triangle) such that the angle $\\angle{AOB} = \\angle{BOC} = \\angle{AOC}$? What do we call this point?

Answer 1

The incenter of a triangle is a triangle center, a point defined for any triangle in a way that is independent of the triangle's placement or scale. The incenter may be equivalently defined as the point where the internal angle bisectors of the triangle cross, as the point equidistant from the triangle's sides, and as the center point of the inscribed circle of the triangle.

Answer 2

Any triangle at all has a 3 angle sum of 180°.