# A good geometry problem

Geometry Level 5

In the diagram below, angle $$ABC$$ is a right angle. Point $$D$$ is on $$\overline{BC}$$, and $$\overline{AD}$$ bisects angle $$CAB$$. Points $$E$$ and $$F$$ are on $$\overline{AB}$$ and $$\overline{AC}$$, respectively, so that $$AE = 3$$ and $$AF=10$$. Given that $$EB = 9$$ and $$FC = 27$$, find the integer closest to the area of quadrilateral $$DCFG$$.

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