A circle has center $G$, and points $M$ and $N$ lie on the circle. Line segments $MH$ and $NH$ are tangent to the circle at points $M$ and $N$, respectively. If the radius of the circle is 800 millimeters, and the perimeter of quadrilateral $GMHN$ is 4,600 millimeters, what is the distance, in millimeters, between points $G$ and $H$?