Question

Where is the circumcenter located in relation to the triangle

Answer 1

The circumcenter is the point of concurrency (intersection) of the three perpendicular-bisectors of the sides of the triangle. It is the center of the circle that can be circumscribed about the triangle. So, the circumcenter would lie inside the triangle, on the triangle, or outside the triangle.
Check the interactive triangle at the link to verify this:
http://www.mathopenref.com/trianglecircumcenter.html