2025 NASS PRELIMS P1 Q26

A plot of land \(ABCD\) is to be used for a park. \(AD=760\text{ m}\), angle \(BCD=52^\circ\), and sides \(AB\) and \(BC\) are shown below at a scale of \(1:20\,000\).

1. On the diagram, construct the plot \(ABCD\).[2]
2. A café is to be built nearer to \(B\) than \(A\), and at most \(1\text{ km}\) from \(C\). Using appropriate constructions, shade the region inside \(ABCD\) where it can be built.[2]
3. A pebbled pathway is a circular arc whose every point is \(400\text{ m}\) from \(B\). Calculate the length of the pathway.[2]