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)$

…???

## Best Answer

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.