A Parallel-Plane Locus in a Cube

Problem

In a cube $ABCD\text{-}A_1B_1C_1D_1$ of edge length $1$ , let $E$ and $F$ be the midpoints of the edges $BC$ and $CC_1$ respectively. A point $P$ moves on the face $ADD_1A_1$ so that $PC_1$ is parallel to the plane $AEF$ .

1. Find the length of the locus of $P$ . 2. Find the minimum distance from $P$ to the line $AF$ .

Answer

Solution

Difficulty	7/10
Topics	Extrema, solid geometry

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