Question acfddb5

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 $168$ millimeters and the perimeter of quadrilateral $GMHN$ is $\mathrm{3,856}$ millimeters, what is the distance, in millimeters, between points $G$ and $H$?