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Geometry Level 5

This figure shows a square $$ABCD$$ of side $$a$$. It contains arcs $$BD$$ and $$AC$$ drawn with centers at $$A$$ and $$D$$, respectively. If $$x$$ is the radius of the circle tangent to $$BC$$ and arcs $$AC$$ and $$BD$$, Then, what is the value of $$\dfrac{x}{a}$$?

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