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Improving a theorem in  we observe that a maximal torus of an extrinsic symmetric space in a euclidean space V is itself extrinsic symmetric in some affine subspace of V. A compact extrinsic symmetric space is a submanifold X ⊂ S p−1 ⊂ R p = V such that for any point x ∈ X the reflection s x along the normal space N = N x X keeps X invariant. Every compact symmetric space X contains a maximal torus T which is unique up to congruence. If X = S n ⊂ R n+1 , the maximal torus is a great circle Cdoi:10.18910/86337 fatcat:lrwqaiaiq5cf7kdxkjxj5wso2y