OMCC 2001 Problem 2

Let $AB$ be the diameter of a circle with a center $O$ and radius $1$ . Let $C$ and $D$ be two points on the circle such that $AC$ and $BD$ intersect at a point $Q$ situated inside of the circle, and $\angle AQB= 2 \angle COD$ . Let $P$ be a point that intersects the tangents to the circle that pass through the points $C$ and $D$ .

Determine the length of segment $OP$ .