2025 CHS PRELIMS P1 Q22

A triangle (XYZ) is shown below.

1. Construct
   1. the perpendicular bisector of (XY),[1]
   2. the bisector of angle (XYZ).[1]
2. Mark clearly a possible point which is inside the triangle, equidistant from (X) and (Y), and nearer to (YZ) than (XY). Label this point (P).[1]
3. The point (M) is such that (angle YZM=100^circ) and (XM=5 ext{ cm}). Mark and label the point (M) at the position that is closer to point (Z). Measure and write down the length (ZM).[2]