# 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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