# 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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