The diagram and the statement 'O is the centre of the bigger circle' are correct, and the lengths OR=24 and OS=18 are incorrect.

The problem statement contains contradictory information, which makes it impossible to solve without making an assumption.

Here's the contradiction:

1. The problem states: "O is the centre of the bigger circle" and "Q, R, S are points on the bigger circle".
2. If R and S are points on the bigger circle and O is its center, then OR and OS must be radii of the bigger circle. Therefore, OR must be equal to OS.
3. However, the problem also states: "OR = 24 and OS = 18". These values are different, which contradicts the fact that OR and OS should be equal radii.

Given this contradiction, I must make an assumption to proceed. I will assume that the diagram and the statement "