NL-NWO 1962 Problem 1

Given a triangle $ABC$ with $\angle C = 90^o$ . a) Construct the circle with center $C$ , so that one of the tangents from $A$ to that circle is parallel to one of the tangents from $B$ to that circle. b) A circle with center $C$ has two parallel tangents passing through A and go respectively. If $AC = b$ and $BC = a$ , express the radius of the circle in terms of $a$ and $b$ .