OCR C2 — Question 8

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
TopicRadians, Arc Length and Sector Area

8.
\includegraphics[max width=\textwidth, alt={}, center]{27703044-8bb3-4809-9454-ae6774fec060-3_501_492_242_607} The diagram shows a circle of radius 12 cm which passes through the points \(P\) and \(Q\). The chord \(P Q\) subtends an angle of \(120 ^ { \circ }\) at the centre of the circle.
  1. Find the exact length of the major arc \(P Q\).
  2. Show that the perimeter of the shaded minor segment is given by \(k ( 2 \pi + 3 \sqrt { 3 } ) \mathrm { cm }\), where \(k\) is an integer to be found.
  3. Find, to 1 decimal place, the area of the shaded minor segment as a percentage of the area of the circle.