The diameter of a recessed ring was measured by using two spherical balls of diameter $d_2$ = $60$ $mm$ and $d_1$ = $40$ $mm$ as shown in the figure.

The distance $H_2$ = $35.55$ $mm$ and $H_1$ = $20.55$ $mm$. The diameter ($D$, in $mm$) of the ring gauge
is _______