IOM 2019, Блиц — Задача 35

OLYMPIAD OF METROPOLISES, Moscow, September 2, 2019 · 2 септември 2019 г.

Условие

Consider a regular square pyramid $SABCD$ (with apex $S$) with $AB = 21$ and $AS = 42$. Points $N$ and $K$ belong to the edges $CD$ and $SC$, respectively, and satisfy $DN : NC = SK : KC = 2 : 5$. Plane $\alpha$ passes through $NK$ and is parallel to $AS$. Find the square of the distance from point $B$ to $\alpha$.

Решение

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Оригинал в Архива: blitz-en-all-task-final.pdf