I know distance ab and cd, but I need the distance co and the angle aob.
Since oa, ob, and oc are all radii of the circle, then they have the same lengths.
Label oa as "r", ad as "x", and dc as "y". Then od is "y - r". Also, aod is a right triangle, with the length of ad known. Can you find a way to use the Pythagorean Theorem to create an equation with the only unknown being "r"? If so, then you can solve for this value.
Once you have the value of r, then you'll have the lengths of all three sides of the isosceles triangle aob, from which you should be able to find the measure of the angle at o.