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The angle between two ships

Source: IMO LongList 1982 - P44

May 16, 2011
searchgeometry unsolvedgeometry

Problem Statement

Let AA and BB be positions of two ships MM and NN, respectively, at the moment when NN saw MM moving with constant speed vv following the line AxAx. In search of help, NN moves with speed kvkv (k<1k < 1) along the line ByBy in order to meet MM as soon as possible. Denote by CC the point of meeting of the two ships, and set AB=d,∠BAC=α,0≤α<π2.AB = d, \angle BAC = \alpha, 0 \leq \alpha < \frac{\pi}{2}. Determine the angle ∠ABC=β\angle ABC = \beta and time tt that NN needs in order to meet MM.
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