A geometry problem by Ashraful Mahin

Geometry Level pending

Two circles touch internally at point \(M\) and the radius of the larger circle is 8 units. The centre of the larger circle lies on the perimeter of the smaller circle. The diameter of the larger circle that passes through the touching point M meets the larger circle at point \(A\). Tangent drawn from \(A\) to the smaller circle touches that at \(B\). Length of \(AB\) is of the form \( \dfrac ab \sqrt2\), where \(a\) and \(b\) are coprime positive integers, find \(a-b\).

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