2026 NASS P2 Q8

The diagram shows two circles that touch at \(C\).

\(A,B\) and \(C\) are points on the smaller circle, diameter \(APC\).

\(C,D\) and \(E\) are points on the larger circle, diameter \(CRE\).

\(APCRE\) and \(BCD\) are straight lines.

Angle \(PBC=0.37\text{ rad}\) and angle \(CRD=2.27\text{ rad}\).

\(BP\) is parallel to \(DR\).

1. Identify another pair of parallel lines.
   Give a reason for each statement you make.[2]
2. Show that triangle \(ABP\) is similar to triangle \(EDR\).
   Give a reason for each statement you make.[3]
3. Let \(O\) be the centre of the smaller circle.
   The radius of the smaller circle is 8 cm.
   1. Show that angle \(BOC=2.138\text{ rad}\), correct to three decimal places.[3]
   2. Hence calculate the length of the minor arc \(BC\).[1]