AUSTRIAN-POLISH 2000 Problem 2

In a unit cube, $CG$ is the edge perpendicular to the face $ABCD$ . Let $O_1$ be the incircle of square $ABCD$ and $O_2$ be the circumcircle of triangle $BDG$ . Determine min $\{XY|X\in O_1,Y\in O_2\}$ .