Question 60
Let $ABC$ be a triangle with $\angle ABC \gt \angle BCA$ and $\angle BCA \ge 30^\circ$. The angle bisectors of $\angle ABC$ and $\angle BCA$ meet the opposite sides of the triangle at the points $D$ and $E$, respectively. The line $BD$ intersects the line $CE$ at $P$. Assume that $PD = PE$ and that the incircle of the triangle $ABC$ has radius 1. Determine the largest possible length of $BC$.