USAMO 1974 Problem 5

A point inside an equilateral triangle with side 1 is a distance $\mathrm{a}, \mathrm{b}, \mathrm{c}$ from the vertices. The triangle $\mathrm{ABC}$ has $\mathrm{BC}=\mathrm{a}, \mathrm{CA}=\mathrm{b}, \mathrm{AB}=\mathrm{c}$. The sides subtend equal angles at a point inside it. Show that sum of the distances of the point from the vertices is 1 .