The circumcenter of a triangle is the point in the plane equidstant from the three vertices of the triangle.

The circumcenter of a triangle is denoted by C.

Since a point equidistant from two points lies on the perpendicular bisector of the segment determined by the two points, C is on the perpendicular bisector of each side of the triangle.

Click here for a GSP script for a circumcenter given any three points (the vertices of the triangle).