Geometry Level 4

A circle of diameter $$14$$ has two identical right triangles that are circumscribed around the two semicircles created by the line $$\overline { AB }$$ cutting the circle in half.

If the short legs of the right triangles are $$11$$ as shown, the length of $$\overline { AB }$$ can be written as $$\frac { a }{ b }$$, where $$a$$ and $$b$$ are co-prime integers. Find $$ab$$.

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