1.15: Isosceles triangle with an inscribed sector

The diagram shows an isosceles triangle $OAB$ such that $OA = OB = 12\text{ cm}$ and angle $AOB = \theta$ radians. Points $C$ and $D$ lie on $OA$ and $OB$ respectively such that $CD$ is an arc of the circle, centre $O$, radius $10\text{ cm}$. The area of the sector $OCD = 35\text{ cm}^2$.