IMO 1982 LL USS50

Let O be the midpoint of the axis of a right circular cylinder.

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IMO 1982 LL USS50

Origin: USS

Problem

Let O be the midpoint of the axis of a right circular cylinder. Let A and B be diametrically opposite points of one base, and C a point of the other base circle that does not belong to the plane OAB. Prove that the sum of dihedral angles of the trihedral OABC is equal to 2\pi.