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Optimization with convex constraints and convex objectives; notions related to convex optimization such as sub-gradients, normal cones, separating hyperplanes

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Inequality $\frac{C}{d_{max}} \le \pi $ relating perimeter and diameter of planar convex body

Let $C$ is a perimeter of a convex hull (plane geometry) and $d_{max}$ is the largest distance of two arbitrary points in the convex hull. I am looking for a proof that: $$\frac{C}{d_{max}} \le \pi …
Đào Thanh Oai's user avatar