IMO 1987 LL TUR62

Let l, l′ be two lines in 3-space and let A, B, C be three points

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IMO 1987 LL TUR62

Origin: TUR

Problem

Let l, l′ be two lines in 3-space and let A, B, C be three points taken on l with B as midpoint of the segment AC. If a, b, c are the distances of A, B, C from l′, respectively, show that b \leq a2+c2 , equality holding if l, l′ are parallel.