2025 NASS PRELIMS P2 Q6

Two circles with centre \(O\) are concentric. \(PQ\) is a diameter of the larger circle and \(RS\) is a diameter of the smaller circle. \(PS\) and \(RQ\) are tangents to the smaller circle.

1. Show that triangle \(PSO\) is congruent to triangle \(QRO\). Give a reason for each statement.[2]
2. The radii of the larger and smaller circles are \(8\text{ cm}\) and \(4.36\text{ cm}\), respectively.
   1. Calculate the area of triangle \(QRO\).[3]
   2. Calculate the shaded area.[4]