A Cube in Motion

Problem

A cube $ABCD\text{-}A_1B_1C_1D_1$ of edge length $2$ moves in a rectangular coordinate system $O\text{-}xyz$ so that the vertex $A$ stays on the $z$ -axis and the vertex $B_1$ stays in the plane $xOy$ . Find the minimum possible length of $OC$ .

Answer

Solution

Difficulty	9/10
Topics	Extrema, solid geometry

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