Circle Circumscribing a Triangle

Given a triangle ABC in R², there is exactly one circle that goes through the points. How do you find the circle?

I'll assume you know how to construct the perpendicular bisector of a line segment.

Any circle that touches both A and B must have its center on the perpendicular bisector of AB.

Similarly, any circle that touches both A and C must have its center on the perpendicular bisector of AC.

The circle we are looking for has its center at the intersection of those two bisectors, and the radius is determined from that center point to any of the three original points.