ABCD is a quadrilateral. Point O is along AD. A semicircle has a diameter along AD.............what is the length of AD?

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ABCD is a quadrilateral. Point O is along AD. A semicircle has a diameter along AD and is tangent to the sides AB, BC, and CD. If AB = 9, CD = 16, and AO = OD, what is the length of AD?

Semicircle AB is flipped upside down and translated horizontally so the new semicircle CD is tangent to AB, as shown. The line through AB is tangent to the semicircle CD and the line through CD is tangent to the semicircle AB.

If each semicircle has a diameter equal to 2, what is the length of AD?
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