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