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\includegraphics[max width=\textwidth, alt={}, center]{616a6177-0d5c-49f7-b0c1-9138a13c1963-3_552_734_255_703}
The diagram shows a circle with radius \(r \mathrm {~cm}\) and centre \(O\). The line \(P T\) is the tangent to the circle at \(P\) and angle \(P O T = \alpha\) radians. The line \(O T\) meets the circle at \(Q\).
- Express the perimeter of the shaded region \(P Q T\) in terms of \(r\) and \(\alpha\).
- In the case where \(\alpha = \frac { 1 } { 3 } \pi\) and \(r = 10\), find the area of the shaded region correct to 2 significant figures.