What does Circumcenter mean?
Use what you know about a perpendicular bisectors to construct a circumcenter below.
1) Find the distance from the Circumcenter to vertex A
2) Repeat this process to vertex B and C
3) What do you notice about each of the distances?
4) What does it mean if a point is equidistant from a given set of points?
Construct a circle from the circumcenter to one of the vertices of the triangle above. This circle is CIRCUMscribed around the triangle. Thus the name Circumcenter.
When you construct a circumcenter, will the circle created from the circumcenter to a vertex ever be inside the triangle?