IMO 1989 LL VIE109

Let Ax, By be two noncoplanar rays with AB as a common per-

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IMO 1989 LL VIE109

Origin: VIE

Problem

Let Ax, By be two noncoplanar rays with AB as a common per- pendicular, and let M, N be two mobile points on Ax and By respectively such that AM + BN = MN. First version. Prove that there exist infinitely many lines coplanar with each of the lines MN. Second version. Prove that there exist infinitely many rotations around a fixed axis ∆mapping the line Ax onto a line coplanar with each of the lines MN.