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\includegraphics[max width=\textwidth, alt={}, center]{1cf37a58-8a7f-4dc8-9e35-2e8badf3eb83-3_293_502_269_826}
The diagram shows the sector \(O P Q\) of a circle with centre \(O\) and radius \(r \mathrm {~cm}\). The angle \(P O Q\) is \(\theta\) radians and the perimeter of the sector is 20 cm .
- Show that \(\theta = \frac { 20 } { r } - 2\).
- Hence express the area of the sector in terms of \(r\).
- In the case where \(r = 8\), find the length of the chord \(P Q\).