4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9f1194cd-cc8a-4f8d-8010-c62fea344c4e-03_681_1237_258_287}
\captionsetup{labelformat=empty}
\caption{Fig. 3}
\end{figure}
Triangle \(A B C\) has \(A B = 9 \mathrm {~cm} , B C 10 \mathrm {~cm}\) and \(C A = 5 \mathrm {~cm}\).
A circle, centre \(A\) and radius 3 cm , intersects \(A B\) and \(A C\) at \(P\) and \(Q\) respectively, as shown in Fig. 3.
- Show that, to 3 decimal places, \(\angle B A C = 1.504\) radians.
Calculate,
- the area, in \(\mathrm { cm } ^ { 2 }\), of the sector \(A P Q\),
- the area, in \(\mathrm { cm } ^ { 2 }\), of the shaded region \(B P Q C\),
- the perimeter, in cm , of the shaded region \(B P Q C\).