Is there some kind of triangle such that the perpendicular bisector of eachside is also an angle bisector, a median, and an altitude?

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter7: Locus And Concurrence
Section7.2: Concurrence Of Lines
Problem 12E
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Is there some kind of triangle such that the perpendicular bisector of each
side is also an angle bisector, a median, and an altitude?

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