IMO 1970 LL NET32

Origin: NET

Problem

Let there be given an acute angle \angleAOB = 3\alpha, where OA = OB. The point A is the center of a circle with radius OA. A line s parallel to OA passes through B. Inside the given angle a variable line t is drawn through O. It meets the circle in O and C and the given line s in D, where \angleAOC = x. Starting from an arbitrarily chosen position t0 of t, the series t0, t1, t2, . . . is determined by defining BDi+1 = OCi for each i (in which Ci and Di denote the positions of C and D, corresponding to ti). Making use of the graphical representations of BD and OC as functions of x, determine the behavior of ti for i \to\infty.