When the Cutting Plane Reaches a Hidden Edge

Problem

As shown in the figure, the cube $ABCD\text{-}A_1B_1C_1D_1$ has edge length $1$ . Points $E$ and $F$ move along the edges $AD$ and $B_1C_1$ respectively, with $AE = x$ and $B_1F = y$ . If the edge $DD_1$ and the plane $BEF$ have at least one common point, find the range of $x + y$ .

Answer

Solution

Difficulty	7/10
Topics	solid geometry, Linear Algebra

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