Different centers of a triangle:
1. In center
It is inside the triangle. This is the point of intersection of angular bisector of the triangle. Denoted by C.
If you extend the sides AC and AB, then the center of circle that is tangent to extended AC, AB and BC. there are 3 for each triangle. It is outside the triangle. Denoted by C1, C2, C3.
3. geometrical center - centroid
intersection of medians of triangle. This is always inside the triangle. Denoted by G.
center of circle on which the vertices of the triangle lie. This can be inside the triangle or outside the triangle. This is also the point of intersection of the perpendicular bisectors of triangles.
point of intersection of all the altitudes of a triangle. denoted by O.