9.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3b99072a-cd16-4c1d-9e44-085926a3ba24-13_460_698_269_625}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
In Figure 3, the points \(A\) and \(B\) are the centres of the circles \(C _ { 1 }\) and \(C _ { 2 }\) respectively. The circle \(C _ { 1 }\) has radius 10 cm and the circle \(C _ { 2 }\) has radius 5 cm . The circles intersect at the points \(X\) and \(Y\), as shown in the figure.
Given that the distance between the centres of the circles is 12 cm ,
- calculate the size of the acute angle \(X A B\), giving your answer in radians to 3 significant figures,
- find the area of the major sector of circle \(C _ { 1 }\), shown shaded in Figure 3,
- find the area of the kite \(A Y B X\).