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Compute the least value of f(p) - ISL 1986

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August 31, 2010
geometry3D geometrytetrahedroncircumcircleIMO Shortlistminimization

Problem Statement

A tetrahedron ABCDABCD is given such that AD=BC=a;AC=BD=b;ABā‹…CD=c2AD = BC = a; AC = BD = b; AB\cdot CD = c^2. Let f(P)=AP+BP+CP+DPf(P) = AP + BP + CP + DP, where PP is an arbitrary point in space. Compute the least value of f(P).f(P).
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