RMM 2008 Problem 1

Let $ABC$ be an equilateral triangle and $P$ in its interior. The distances from $P$ to the triangle's sides are denoted by $a^2, b^2,c^2$ respectively, where $a,b,c>0$ . Find the locus of the points $P$ for which $a,b,c$ can be the sides of a non-degenerate triangle.