MathDB

6

Part of 1976 IMO Longlists

Problems(1)

Sum of distances of point from all faces of polytope

Source:

1/3/2011
For each point XX of a given polytope, denote by f(X)f(X) the sum of the distances of the point XX from all the planes of the faces of the polytope. Prove that if ff attains its maximum at an interior point of the polytope, then ff is constant.
functioninequalities unsolvedinequalities