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A convex polygon $$\Gamma$$ is such that the distance between any two vertices of $$\Gamma$$ does not exceed 1.

• Prove that the distance between any two points on the boundary of $$\Gamma$$ does not exceed 1.
• If X and Y are two distinct points inside $$\Gamma$$, prove that there exists a point Z on the boundary of $\\Gamma$ such that $$XZ + YZ \leq 1$$

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