OPM 2023 Problem 2

Let $[AB]$ be a diameter of a circle with center $O$ and radius $1$ . Consider $P$ a point on the circumference, different from $A$ and $B$ and let $Q$ be the midpoint of the arc $AP$ . The line parallel to $PQ$ that passes through $O$ intersects the line $PB$ at point $S$ . Determine $\overline{PS}$ .