SHARYGIN 2008 Problem 21
(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?
Dataset text AI-MO AoPS. Quoted with source.
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