Ken's Puzzle of the Week

Circle in a Cube

What is the largest circle you can construct in a unit cube?

Source: Based upon the IBM Ponder This puzzle for May 2007.

Solutions were received from Earl Gose, Kevin Haborak, Joseph DeVincentisRadu Ionescu, Dan Dima, K Sengupta.  Most determined the largest circle to be the one inscribed in the hexagon created by joining the midpoints of the sides of the cube across all six faces (hexagon side length sqrt(2)/2).  The inscribed circle has a diameter of sqrt(3/2).
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