TH-TMO 2013 Problem 2

Let $\vartriangle ABC$ be a triangle with $\angle ABC > \angle BCA \ge 30^o$ . The angle bisectors of $\angle ABC$ and $\angle BCA$ intersect $CA$ and $AB$ at $D$ and $E$ respectively, and $BD$ and $CE$ intersect at $P$ . Suppose that $P D = P E$ and the incircle of $\vartriangle ABC$ has unit radius. What is the maximum possible length of $BC$ ?