2025 SST PRELIMS P1 Q23

The diagram shows a plot of land \(PTVU\). \(PT\) and \(PU\) are tangents to an arc of a circle at \(T\) and \(U\).

1. Find the centre of the circle and label it \(X\).[1]
2. Construct the perpendicular bisector of \(TP\).[1]
3. Construct the angle bisector of \(\angle TPU\).[1]
4. A lookout tower is to be built within \(PTVU\), nearer to \(T\) than \(P\), and nearer to \(PT\) than \(PU\). Shade the possible region.[1]