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1/2 \sqrt{a^2 +b^2 +c^2} is max distance in interior point of parallelepiped

Source: Polish second round 1996 p6

January 19, 2020
parallelepipeddistance3D geometrygeometry

Problem Statement

Prove that every interior point of a parallelepiped with edges a,b,ca,b,c is on the distance at most 12a2+b2+c2\frac12 \sqrt{a^2 +b^2 +c^2} from some vertex of the parallelepiped.
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