5 The diagram shows a sector \(O P Q\) of a circle with centre \(O\).
\includegraphics[max width=\textwidth, alt={}, center]{a5fa3066-e330-46d0-98e3-92d438ed6f61-3_305_531_1105_758}
The radius of the circle is 18 m and the angle \(P O Q\) is \(\frac { 2 \pi } { 3 }\) radians.
- Find the length of the arc \(P Q\), giving your answer as a multiple of \(\pi\).
- The tangents to the circle at the points \(P\) and \(Q\) meet at the point \(T\), and the angles \(T P O\) and \(T Q O\) are both right angles, as shown in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{a5fa3066-e330-46d0-98e3-92d438ed6f61-3_597_529_1848_758}
- Angle \(P T Q = \alpha\) radians. Find \(\alpha\) in terms of \(\pi\).
- Find the area of the shaded region bounded by the \(\operatorname { arc } P Q\) and the tangents \(T P\) and \(T Q\), giving your answer to three significant figures.