In circle $O$, a chord $AB$ and a radius $OC$ are drawn such that $C$ is the midpoint of chord $AB$. Given that the radius of the circle is $12$ units, and the distance from the center $O$ to the chord $AB$ is $9$ units, we want to find the length of the chord $AB$.

Use the formula for the segment of a circle, or apply the Pythagorean theorem based on the right triangle $OAC$, where $A$ is one endpoint of the chord and $C$ is the foot of the perpendicular dropped from $O$ to $AB$.