CAIE P1 2016 November — Question 5

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2016
SessionNovember
TopicRadians, Arc Length and Sector Area

5
\includegraphics[max width=\textwidth, alt={}, center]{5fed65b9-a848-4343-858c-3cbac0608b24-2_609_533_938_804} The diagram shows a major arc \(A B\) of a circle with centre \(O\) and radius 6 cm . Points \(C\) and \(D\) on \(O A\) and \(O B\) respectively are such that the line \(A B\) is a tangent at \(E\) to the arc \(C E D\) of a smaller circle also with centre \(O\). Angle \(C O D = 1.8\) radians.
  1. Show that the radius of the \(\operatorname { arc } C E D\) is 3.73 cm , correct to 3 significant figures.
  2. Find the area of the shaded region.