Given a point A and a circle c1 with center O and point B on c1. Construct (with straightedge and compass) a circle c2 which passes through A and which is tangent to c1 at B.

Given two rays OA and OB and a point OA’ on ray OA. If |OA| = a, |OA’| = 9/a, |OB| =3, and |AB| =c, what is |A’B|? Prove your answer is correct.