# Playing with Right-Angled Triangles!

Geometry Level 4

Let $$ABC$$ be a right-angled triangle with hypotenuse $$AB$$ and altitude $$CF$$, where $$F$$ lies on $$AB$$. The circle through $$F$$ centred at $$B$$ and another circle of the same radius centred at $$A$$ intersect on the side $$CB$$. If the ratio between the lengths of $$FB$$ and $$BC$$ can be expressed as $$\left( \dfrac{A}{B} \right)^{C/D}$$, for positive integers $$A,B,C,D$$, find the minimum value of $$A+B+C+D$$.

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