CEMC Fermat, 2006

Geometry Difficulty 3.0 AMC 10/12 Find the answer Canada

In the diagram, $\triangle ABC$ is right-angled. Side $AB$ is extended in each direction to points $D$ and $G$ such that $DA = AB = BG$ . Similarly, $BC$ is extended to points $F$ and $K$ so that $FB = BC = CK$ , and $AC$ is extended to points $E$ and $H$ so that $EA = AC = CH$ . The ratio of the area of the hexagon $DEFGHK$ to the area of $\triangle ABC$ is

(A) $4:1$ (B) $7:1$ (C) $9:1$ (D) $16:1$ (E) $13:1$

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