1.42: Past-paper question 3

Figure 1 shows circle $\displaystyle C_1$ with radius 7 cm and circle $\displaystyle C_2$ with centre $\displaystyle O$ and radius 7 cm

The circles $\displaystyle C_1$ and $\displaystyle C_2$ intersect at the point $\displaystyle A$ and at the point $\displaystyle B$

The size of angle $\displaystyle AOB$ is $\displaystyle \theta$ radians

The perimeter of the region $\displaystyle R$ shown shaded in Figure 1 is $\displaystyle \frac{28\pi}{9}$ cm

(a) Find the exact value of $\displaystyle \theta$

(b) Find the area, in $\displaystyle \mathrm{cm}^2$ to 3 significant figures, of the region $\displaystyle R$