<s>[INST] Area stacked between common tangent and circles Is there any way to find area of shaded region?

The radii of circles are $4$ and $12$ units.
 [/INST] 
By similar triangles, $CD=8$.
By Pythagoras' Theorem, $CG=EF=8\sqrt{3}$
Area of trapezoid $ACEF=\frac{(4+12)\times 8\sqrt{3}}{2}=64\sqrt{3}$
$\angle BAF=\cos^{-1} \left(  \frac{1}{2} \right)=60^{\circ}$ and 
$\angle BCE=180^{\circ}-60^{\circ}=120^{\circ}$
$\therefore$ area of sector $BAF
=\pi (12)^{2} \times \frac{60^{\circ}}{360^{\circ}}
=24\pi$
$\therefore$ area of sector $BCE
=\pi (4)^{2} \times \frac{120^{\circ}}{360^{\circ}}
=\frac{16\pi}{3}$
The required area $=64\sqrt{3}-24\pi-\frac{16\pi}{3}
                   =64\sqrt{3}-\frac{88\pi}{3}$
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