A Chord Through Two Centroids

Problem

In a cube $ABCD\text{-}A_1B_1C_1D_1$ with edge length $3$ , let $E$ and $F$ be the centroids of $\triangle A_1DB$ and $\triangle A_1DC_1$ respectively. Find the length of the chord cut from the circumscribed sphere of the cube by the line through $E$ and $F$ .

Answer

Solution

Difficulty	6/10
Topics	solid geometry, Circles

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