2
\includegraphics[max width=\textwidth, alt={}, center]{fbe396af-4d5b-4c3f-b528-b2e0783c7bc4-02_579_895_817_625} A sector \(O A B\) of a circle of radius \(r \mathrm {~cm}\) has angle \(\theta\) radians. The length of the arc of the sector is 12 cm and the area of the sector is \(36 \mathrm {~cm} ^ { 2 }\) (see diagram).

1. Write down two equations involving \(r\) and \(\theta\).
2. Hence show that \(r = 6\), and state the value of \(\theta\).
3. Find the area of the segment bounded by the arc \(A B\) and the chord \(A B\).