IOM 2020, Блиц — Задача 45

The Blitz-contest of IOM-2020

Условие

A sphere is inscribed in a right circular cone. The angle between the generating line of the lateral surface of the cone and its base is $60^{\circ}$. Denote the volume of the cone by $V_1$. Let $B$ be the convex body spanned by the tangency points of the sphere with the cone, including the tangency point with the base (i.e., $B$ is the convex hull of these points).

Denote the volume of the body $B$ by $V_2$. Determine $V_1/V_2$.

Fractional numbers can be entered either as a decimal fraction or as $m/n$.

Отговори

Решение

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Оригинал в Архива: iom-2020-blitz-tasks.pdf · официални решения: iom-2020-blitz-answers.pdf