IMO 1974 LL USA37

Let a, b, and c denote the three sides of a billiard table in the

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IMO 1974 LL USA37

Origin: USA

Problem

Let a, b, and c denote the three sides of a billiard table in the shape of an equilateral triangle. A ball is placed at the midpoint of side a and then propelled toward side b with direction defined by the angle \theta. For what values of \theta will the ball strike the sides b, c, a in that order?