Which of the following is the area of the yellow region?

Let $X$ be the center of the smaller circle. Draw $AX$ as shown. Let $r=AX=XG=FX=OC$ , $y=OX$ and $x=AO$ . Then we have

$r+y=\dfrac{2r+9}{2}$ $\implies$ $2r+2y=2r+9$ $\implies$ $2y=9$ $\implies$ $y=4.5$

and

$x+5=y+r$ $\implies$ $x=-5+4.5+r$ $\implies$ $x=r-0.5$

By pythagorean theorem on $\triangle AOX$ , we have

$r^2=x^2+y^2=r^2-r+0.25+20.25$ $\implies$ $0=-r+20.5$ $\implies$ $r=20.5$

Let $R=OE=OG=OB=OD$ , then $R=r+y=20.5+4.5=25$

Thus, the area of the yellow region is

$A=\pi (R^2-r^2)=\pi (25^2-20.5^2)=\boxed{204.75 \pi}$