40 - 120

In triangle $ABC$, the angle $A \hat{B C}$ measures $20^{\circ}$ and the angle $A \hat{C} B$ measures $40^{\circ}$. Let $E$ be a point on $BC$ such that $BE = BA$.

(a) Show that triangle CEA is isosceles.

(b) Knowing that the length of the angle bisector of angle BÂC is 2, determine $\mathrm{BC}-\mathrm{AB}$.