A geometry problem by Dexter Woo Teng Koon

The points $A$ , $B$ , $C$ and $D$ are the centers of the circles as shown above. The line $EF$ is the tangent line to the 2 big circles. $CA=AB=BD$ . Line $CD$ is parallel to line $EF$ .

If the area of the blue section is 1, find the area of the red section.

Give your answer in the nearest 3 decimal places.

Inspiration .