IMO 1982 LL TUN44

Let A and B be positions of two ships M and N, respectively,

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IMO 1982 LL TUN44

Origin: TUN

Problem

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, \angleBAC = \alpha, 0 \leq\alpha < \pi 2 . Determine the angle \angleABC = \beta and time t that N needs in order to meet M.