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distance independent of n points on ellipsoid

Source: VJIMC 1999 1.3

July 28, 2021
geometry

Problem Statement

Let A1,…,AnA_1,\ldots,A_n be points of an ellipsoid with center OO in Rn\mathbb R^n such that OAiOA_i, for i=1,…,ni=1,\ldots,n, are mutually orthogonal. Prove that the distance of the point OO from the hyperplane A1A2…AnA_1A_2\ldots A_n does not depend on the choice of the points A1,…,AnA_1,\ldots,A_n.
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