IMO 1986 LL FIN20

For any angle lpha with 0 < lpha < 180◦, we call a closed convex

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IMO 1986 LL FIN20

Origin: FIN

Problem

For any angle \alpha with 0 < \alpha < 180◦, we call a closed convex planar set an \alpha-set if it is bounded by two circular arcs (or an arc and a line segment) whose angle of intersection is \alpha. Given a (closed) triangle T , find the greatest \alpha such that any two points in T are contained in an \alpha-set S \subsetT .