A surprising answer

Geometry Level 5

In the diagram, the circle centered at \(B\) and the circle centered at \(O\) are tangent inside square \(ABCD\). If \(\cos{\angle{OBC}}=\frac{a}{b}\) for coprime positive integers \(a\) and \(b\), then what is \(a+b\)?

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Zhou ZeHao by Zhou ZeHao
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