1.5: Exact area enclosed by two circles

Figure 1 shows two circles, $\displaystyle C_1$ and $\displaystyle C_2$, each with a radius of $\displaystyle 6\,\mathrm{cm}$.

The centre of $\displaystyle C_1$ is $\displaystyle O_1$ such that $\displaystyle O_1$ lies on $\displaystyle C_2$. The centre of $\displaystyle C_2$ is $\displaystyle O_2$ such that $\displaystyle O_2$ lies on $\displaystyle C_1$.

The circles intersect at the points $\displaystyle A$ and $\displaystyle B$ and enclose the region $\displaystyle R$, shown shaded in Figure 1.

The area of region $\displaystyle R$ is $\displaystyle P\,\mathrm{cm}^2$.

Find the exact value of $\displaystyle P$, giving your answer in the form

where $\displaystyle a$, $\displaystyle b$ and $\displaystyle c$ are integers.