Consider sector of circle $MAB$. $∠AMB = 120◦$.
A circle $S$ touches side $AM$, side $MB$ and arc $AB$ as shown in the ﬁgure.
Area of circle $S$ is $75π/(7 + 4√3)$ . Find $4√3$ times the area of $△AMB$.
Here , I know the area of circle , so radius can be calculated. For triangle $AMB$ , it's area is equal to $1/2*AM^2*\sin 120$(degrees). So I just require the length of $AM$, that is the radius of sector.
$AM$ and $MB$ are tangents to the circle so that may be of some help? But I'm stuck here .
Any hints are apreciated . (This is not class-homework , I'm solving sample questions for a competitive exam )