Suppose ABCD is an isosceles trapezoid with bases AB and CD and sides AD and BC such that |CD| > |AB|. Also suppose that |CD| = |AC| and that the altitude of the trapezoid is equal to |AB|

If |AB|/|CD| = a/b where a and b are positive coprime integers, then find a^b?

In rectangle ABCD, a semicircle CPS is drawn as shown below.
The semicircle’s diameter is shared with and extends beyond side BC, it intersects side AB at Q, and it is tangent to side AD at S.
If CQ = 10, what is the area of rectangle ABCD?

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?