OME 2002 Problem 2

In the triangle $ABC$ , $A'$ is the foot of the altitude to $A$ , and $H$ is the orthocenter. $a)$ Given a positive real number $k = \frac{AA'}{HA'}$ , find the relationship between the angles $B$ and $C$ , as a function of $k$ . $b)$ If $B$ and $C$ are fixed, find the locus of the vertice $A$ for any value of $k$ .