# Geometry?

Geometry Level 5

$\large \min{\left|\frac{x_i-x_j}{1+x_ix_j}\right|} \leq C$

For all 7-tuples of real numbers $$(x_1, x_2,...,x_7)$$, the following inequality holds, where the minimum is taken over all $$1 \leq i < j \leq 7$$. Let $$D$$ be the smallest possible value of $$C$$. If we can have $$\min{\left|\dfrac{x_i-x_j}{1+x_ix_j}\right|} = D$$, submit your answer as $$\dfrac{1}{D^2} + 2017$$. If not, then submit your answer as $$\dfrac{1}{D^2} + 1$$.

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