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Consider three distinct vectors $x,y$ and $z$. Prove that the equation $$\left\|x-y\right\|\left\|z\right\|=\left\|y-z\right\|\left\|x\right\|+\left\|z-x\right\|\left\|y\right\|$$ holds if and only if the four points $x,y,z,0$ are contained on a circle such that the pairs $x,y$ and $z,0$ separe each other

Many thanks in advance for the help.

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    What is a circle in an inner product space? – 2017-01-07
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    What space are you working in? – 2017-01-07
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    This problem is in the book Linear Algebra of W.H. Greub, in the section of Inner product spaces. – 2017-01-07

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