Tangent Circle

Geometry Level 5

Let \( ABC\) be a triangle with sides \( AB=7\), \( BC=11\) and \( CA=12\), and let \( \omega_a\) be the circle tangent to \(AB\), \(AC\) at the points \(D\), \(E\) and internally tangent to the circumscribed circle \( \odot ABC\). What is the length of the segment \( AD\)?

Details and Assumptions

Assuming that the length of the segment \(AD\) is the simple fraction \(\frac{a}{b}\) , type the sum \(a+b\) as your answer.

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