The circumcenter is equidistant from the three vertices of the triangle. From the figure shown, we will prove DA = DB = DC.
1) Triangle ABC; Perpendicular bisectors of each side(Given)
2) DA = DB, DC = DB(If a point is on the perp. bisector of a segment, it is equidistant from each endpoint of the segment.)
3) DA = DB(Substitution)\
4) D is on the perpendicular bisector of seg. AB(Converse of 2)
5)DA = DB = DC, so D is equidistant from
the 3 vertices of the triangle(Steps 2 and 3 and definition