Its in the top

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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