Perpendicular Bisectors of Triangle Sides

Formulas, in terms of the sidelengths and area, are given for the lengths of the segments of the perpendicular bisectors of the sides of a tria n- gle in its interior. The ratios of perpendicular bisector segments to each othe r are given, and the ratios of the segments into which the perpendicular bisectors are divided by the circumcenter are considered. Then we ask whether a set of three perpendicular bisector lengths uniquely determines a triangle. The answer is no in general: depending on the set of bisectors, anywhere from zero to four (but no more than four) triangles can share the same perpendicular bisector segments.