2025 CGSS PRELIMS P2 Q5

The figure shows a semi-circle \(AOBD\) with centre \(O\), and \(OP\) is perpendicular to \(BD\). \(BC\) and \(CD\) are tangents to the semi-circle at \(B\) and \(D\).

1. Show that triangles \(ABD\) and \(OBP\) are similar. Give a reason for each statement you make.[2]
2. Find the ratio \(\dfrac{\text{area of triangle}\hspace{0.5em}OBP}{\text{area of triangle}\hspace{0.5em}AOD}\).[2]
3. Show that angle \(BOD=2.2689\) radians, correct to 5 significant figures.[2]
4. It is given that the radius of the semi-circle is \(4\text{ cm}\) and \(BC=8.58\text{ cm}\). Calculate
   1. the perimeter of the shaded part,[2]
   2. the area of the shaded part.[3]