Two circles has a common centre, \(O\). Points \(\mathrm{A}\) and \(\mathrm{B}\) lie on the circumference of the larger circle, which has radius \(\mathrm{OA} = R\). Points \(\mathrm{C}\) and \(\mathrm{D}\) line on \(\mathrm{[OB]}\) and \(\mathrm{[OA]}\) respectively, and they also lie on the circumference of the smaller circle. The smaller circle has radius \(\mathrm{OC} = r\) and the acute angle \(\mathrm{D\hat{O}C} = \mathrm{A\hat{O}B} = \theta\) radians.
This is shown in the following diagram.
The area of the sector \(\mathrm{OAB}\) is \(50\) cm\(^2\) and its perimeter is \(40\) cm. The area of the sector \(\mathrm{ODC}\) is \(18\) cm\(^2\).
Find the value of \(\theta\).
[5]Hence, find the value of \(r\).
[2]Need help? Join our JC Math tuition classes.
Learn more