Not your average shuriken

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 \(ab\).

Try another geometry problem: "Star Stumper".
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