2025 MSHS PRELIMS P1 Q4

The diagram shows a segment of a circle, \(PQR\).

1. A point \(X\) on the perimeter of the segment is such that \(PX=RX\). Find and label the position of \(X\).[1]
2. On the diagram, construct the angle bisector of angle \(XPR\).[1]
3. On the diagram, shade a region inside \(PQR\) that is closer to \(PR\) than \(PX\), and closer to \(P\) than \(R\).[1]