The point formed by the perpendicular bisectors is the circumcenter. Each segment of the triangle acts as a chord of some circle. All chords are perpendicular to a unique radius of a circle. The intersection of three such chord-perpendiculars gives us a unique circle. A right triangle puts the circumcenter on the hypotenuse, an acute triangle puts the circumcenter in the interior of the triangle and an obtuse triangle will have a circumcenter exterior of the triangle.