IMO 1978 LL YUG54

Let p, q and r be three lines in space such that there is no plane

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IMO 1978 LL YUG54

Origin: YUG

Problem

Let p, q and r be three lines in space such that there is no plane that is parallel to all three of them. Prove that there exist three planes \alpha, \beta, and \gamma, containing p, q, and r respectively, that are perpendicular to each other (\alpha \perp\beta, \beta \perp\gamma, \gamma \perp\alpha).