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
of equidistant)