Calculate the area of intersection between the circles below as a function of A1 and A2.

For reference:In the figure, calculate the area of intersection between the circles as a function of $A1$ and $A2$. $OT = TO1$

My progress

$S=S_1+S_2\\ A_1 = \pi R^2\\ A_2 =\pi r^2\\ R=2r \therefore A_1 = \pi (2r)^2 = 4r^2\pi\\ S_1=S_{GEO_1F}=S_{OEO_1F}-S\triangle_{OEF}=S_{OEO_1F}-\frac{EF.GO}{2}\\ S_2=S_{GFTE}=S_{TEO_1F}-S\triangle_{_1OEF}= S_{TEO_1F}-\frac{EF.GO_1}{2}\\ S_1+S_2 = S_{OEO_1F}-\frac{EF.GO}{2}+ S_{TEO_1F}-\frac{EF.GO_1}{2}= S_{OEO_1F}+S_{TEO_1F}-\frac{EF}{2}(\underbrace{GO_1+GO}_R)$

...???

As per the answer key you provided (in comments), it seems you have misunderstood the question. $A_1$ and $A_2$ are not the areas of full circles, they are areas of the crescents!

With this hint, you can find the answer easily.

$$A+A_1=4\pi r^2$$ $$A+A_2=\pi r^2$$ where $r$ is the radius of smaller circle. Find $A$.