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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