2026 RSS P2 Q5

The diagram shows a circle with centre \(O\) and radius \(6\) cm.

\(A\), \(Q\), \(B\) and \(C\) lie on the circle.

\(PA\) and \(PB\) are tangents to the circle at \(A\) and \(B\) respectively.

\(O\), \(R\), \(Q\) and \(P\) lie on a straight line.

Angle \(ACB=1\) radian.

1. Show that triangle \(AOP\) is congruent to triangle \(BOP\). Give a reason for each statement you make.[3]
2. State the value of angle \(AOB\) in radians. Give a reason for your answer.[2]
3. Find the area of the shaded region.[4]