MathDB

There is an equilateral triangle with side

d{}

and a point

P{}

such that the distances from

P{}

to the vertices of the triangle are positive numbers

a, b, c

. Prove that there exist a point

Q{}

and an equilateral triangle with side

a{}

, such that the distances from

Q{}

to the vertices of this triangle are

b, c, d

.
Alexandr Evnin

Problem Statement