TH-TMO 2007 Problem 1

In a circle  $\odot O$ , radius $OA$ is perpendicular to radius $OB$ . Chord $AC$ intersects $OB$ at $E$ so that the length of arc $AC$ is one-third the circumference of   $\odot O$ . Point $D$ is chosen on $OB$ so that $CD \perp AB$ . Suppose that segment $AC$ is $2$ units longer than segment $OD$ . What is the length of segment $AC$ ?