Question

Geometry question :
Under what conditions will
1) the circumcenter
2) the centroid
3) the incenter
4) the orthocenter
5) the excenter
of a triangle lie in the interior of the angle?
Need proof. Please, help

Answer 1

Hence, only case 2, i.e. an acute triangle has circumcenter lies inside the triangle. But how to prove?

Answer 2

@DanJS