Let $$ω$$ be a semicircle with AB as the bounding diameter and let $$CD$$ be a variable chord of the semicircle of constant length such that $$C, D$$ lie in the interior of the arc $$AB$$. Let $$E$$ be a point on the diameter $$AB$$ such that $$CE$$ and $$DE$$ are equally inclined to the line $$AB$$. Prove that
(a) the measure of $$\angle CED$$ is a constant;
(b) the circumcircle of triangle CED passes through a fixed point.