Cube and Circles

A circle is inscribed in a face of a cube of side a. Another circle is circumscribed about a neighboring face of the cube. Find the least distance between points of the circles?

Source: Mekh-Mat Entrance Examinations Problems, Ilan Vardi, Institut des Hautes Études Scientifiques, January 2000, which, in turn cites Smurov, Balsanov, 1986, and A. Shen, personal communications, 1999.

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