Douglas W. Mitchell, Perpendicular bisectors of triangle sides,
Forum Geometricorum, 13 (2013) 53--59.
Abstract. 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 triangle in its interior. The ratios of perpendicular bisector segments to each other 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.
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