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Attempt:

Ok im more sk having trouble proving that the respective points belong to its condition. Such as thr interior. I know will be all points in thr plane of X, but how can i show that all thise points are the interior if S? All i can think of is letting a point, call it "y", be in thr B(r,a) and showing that it is a interior point through the triangle inequality manipulation. But that doesn't use the fact of orthogonality in the set.