4.02: Sector perimeter and area
\(A\), \(B\) and \(C\) lie on a circle with centre \(O\) and radius \(r\). Angle \(AOB=\alpha\) radians.
(a)[4]
The perimeter of the shaded sector equals the length of the major arc \(ACB\). Find the exact value of \(\alpha\).
See the official mark scheme below.
(b)[4]
The area of the shaded sector is \(18(\pi^2-1)\). Find the exact value of \(r\), simplifying your answer.
See the official mark scheme below.
