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Suppose I have an inscribed simplex which has $(n+1)$ vertices, and the diameter of the hypersphere is $d$. I have a point $x$ inside this simplex, is it true that the distance between $x$ and $x$ is nearest to vertex is not greater than $\frac{d}{2}$ ?

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    it should be not larger than d/2, thanks for your comments.2010-12-21

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