2026 DSS P1 Q13

The diagram shows a park in the shape of a quadrilateral \(ABCD\).

Scale: 1 cm to 20 m.

1. Construct the perpendicular bisector of \(AB\).[1]
2. Construct the bisector of angle \(ABC\).[1]
3. A statue \(S\) is to be built in the park. The statue is equidistant from \(A\) and \(B\) and equidistant from \(AB\) and \(CB\).
   Mark and label point \(S\) on the diagram.[1]
4. A running track is to be built in the park. Every part of the track is equidistant from point \(S\). The track meets \(AB\) and \(BC\) at \(X\) and \(Y\) respectively.
   Calculate the length, in metres, of the running track.[2]