In a circle with center $O$, a chord $AB$ has length $16$. A point $M$ is the midpoint of $AB$, and $OM$ is the distance from the center to the chord. Given that the radius of the circle is $r = 10$, and a second chord $CD$ is drawn such that it is perpendicular to $AB$ at point $P$, where $P$ lies on $AB$ such that $AP = 2$. What is the distance $OP$?