lenth of perpendicular bisectors
Source: Sharygin contest 2008. The correspondence round. Problem 21
September 3, 2008
geometry proposedgeometry
Problem Statement
(A.Zaslavsky, B.Frenkin, 10--11) In a triangle, one has drawn perpendicular bisectors to its sides and has measured their segments lying inside the triangle.
a) All three segments are equal. Is it true that the triangle is equilateral?
b) Two segments are equal. Is it true that the triangle is isosceles?
c) Can the segments have length 4, 4 and 3?