IMO 1976 LL YUG51

Four swallows are catching a fly. At first, the swallows are

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IMO 1976 LL YUG51

Origin: YUG

Problem

Four swallows are catching a fly. At first, the swallows are at the four vertices of a tetrahedron, and the fly is in its interior. Their maximal speeds are equal. Prove that the swallows can catch the fly.