Within equilateral triangle $A,$ circle $B$ is inscribed; within circle $B,$ square $C$ is inscribed; within

Within equilateral triangle $A,$ circle $B$ is inscribed; within circle $B,$ square $C$ is inscribed; within square $C,$ circle $D$ is inscribed; within circle $D,$ square $E$ is inscribed; within square $E,$ circle $F$ is inscribed; finally, within circle $F,$ equilateral triangle $G$ is inscribed.

What is the ratio of the area of triangle $A$ to the area of triangle $G?$

(A) $4\sqrt2 : 1$
(B) $8 : 1$
(C) $8\sqrt2 : 1$
(D) $16 : 1$
(E) $16 \sqrt2 : 1$

Answer: D

Source: Manhattan GMAT

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