MathDB
IMO LongList 1987 - Geometric inequality

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September 6, 2010
inequalitiesgeometry proposedgeometry

Problem Statement

Let l,l′l, l' be two lines in 33-space and let A,B,CA,B,C be three points taken on ll with BB as midpoint of the segment ACAC. If a,b,ca, b, c are the distances of A,B,CA,B,C from l′l', respectively, show that b≤a2+c22b \leq \sqrt{ \frac{a^2+c^2}{2}}, equality holding if l,l′l, l' are parallel.
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