12.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e878227b-d625-4ef2-ac49-a9dc05c5321a-28_549_542_212_703}
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\caption{Figure 1}
\end{figure}
Diagram NOT drawn to scale
Figure 1 shows the plan for a pond and platform. The platform is shown shaded in the figure and is labelled \(A B C D\).
The pond and platform together form a circle of radius 22 m with centre \(O\).
\(O A\) and \(O D\) are radii of the circle. Point \(B\) lies on \(O A\) such that the length of \(O B\) is 10 m and point \(C\) lies on \(O D\) such that the length of \(O C\) is 10 m . The length of \(B C\) is 15 m .
The platform is bounded by the arc \(A D\) of the circle, and the straight lines \(A B , B C\) and \(C D\).
Find
- the size of the angle \(B O C\), giving your answer in radians to 3 decimal places,
- the perimeter of the platform to 3 significant figures,
- the area of the platform to 3 significant figures.