1.3: Isosceles triangle with an inscribed arc

The diagram shows an isosceles triangle $OAB$ such that $OA = OB$ and angle $AOB = \theta$ radians. The points $C$ and $D$ lie on $OA$ and $OB$ respectively. $CD$ is an arc of length $9.6\text{ cm}$ of the circle, centre $O$, radius $12\text{ cm}$. The arc $CD$ touches the line $AB$ at the point $M$.