Angle Relationships in Triangle Bisectors and Altitudes

In triangle $ABC$, let $\angle A = \alpha$. Determine the angle between:
a) the angle bisectors of angles $B$ and $C$;
b) the altitudes from vertices $B$ and $C$ (denote these altitudes as $BM$ and $CH$).
In part b), consider the cases where $\alpha < 90^\circ$ and $\alpha > 90^\circ$ separately.