# Triangulo loco

Geometry Level 4

Let $$ABCD$$ be a square of side length 2, $$E$$ is the midpoint of $$DC$$, $$EC$$ is the radius of the circle. The circle cuts $$EB$$ in $$F$$ and the extension of $$FC$$ cuts $$AB$$ in $$G$$.

Find the area of $$\triangle FGB$$.

If the area can be written as $$\dfrac{ a \sqrt{b}-c}{d}$$, where $$a$$ and $$c$$ are positive integer, with $$b$$ and $$d$$ are primes. Submit your answer as $$a+b+c+d$$.

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