- A sector \(A O B\), of a circle centre \(O\), has radius \(r \mathrm {~cm}\) and angle \(\theta\) radians.
Given that the area of the sector is \(6 \mathrm {~cm} ^ { 2 }\) and that the perimeter of the sector is 10 cm ,
- show that
$$3 \theta ^ { 2 } - 13 \theta + 12 = 0$$
- Hence find possible values of \(r\) and \(\theta\).
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