2025 AHS PRELIMS P2 Q10

In the diagram, triangle \(ABC\) is a right-angled triangle. \(AB=9\text{ cm}\), \(BC=12\text{ cm}\) and \(AC=15\text{ cm}\). A circle with centre \(O\) and radius \(3\text{ cm}\) is inscribed inside triangle \(ABC\). The circle touches the sides of the triangle at \(X\), \(Y\) and \(Z\) respectively.

1. Show that the obtuse angle \(YOZ=2.50\) radians, correct to 3 significant figures.[2]
2. Find the perimeter of the major segment \(YXZ\).[4]