# A geometry problem by Isaac Arce Aguilar

Geometry Level 2

In a square $$ABCD$$, $$E$$ and $$F$$ are the midpoints of sides $$AB$$ and $$AD$$, respectively. A point $$G$$ is taken on segment $$CF$$ in such a way that $$2CG=3FG$$.

If the side of the square is $$2$$, then what is the area of $$\triangle{BEG}$$?

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