Question

What are the properties of the circumcenter of a triangle?

Answer 1

The circumcenter of an acute triangle is inside the triangle.
The circumcenter of an obtuse triangle is outside the triangle
The circumcenter of a right triangle is at the center of the hypotenuse

Answer 2

it is the intersection of the perpendicular bisectors of the three sides of the triangle
it is the center of the circle that passes by the three vertices of the triangle

Answer 3

http://en.wikipedia.org/wiki/Circumscribed_circle