ISL 1982 Problem 44

Let $A$ and $B$ be positions of two ships $M$ and $N$ , respectively, at the moment when $N$ saw $M$ moving with constant speed $v$ following the line $Ax$ . In search of help, $N$ moves with speed $kv$ ( $k < 1$ ) along the line $By$ in order to meet $M$ as soon as possible. Denote by $C$ the point of meeting of the two ships, and set $$AB = d, \angle BAC = \alpha, 0 \leq \alpha < \frac{\pi}{2}.$$ Determine the angle $\angle ABC = \beta$ and time $t$ that $N$ needs in order to meet $M$ .