CAIE P1 2005 November — Question 2

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2005
SessionNovember
TopicCircles

2
\includegraphics[max width=\textwidth, alt={}, center]{933cdfe1-27bb-450d-8b9a-b494916242cb-2_625_582_397_778} In the diagram, \(O A B\) and \(O C D\) are radii of a circle, centre \(O\) and radius 16 cm . Angle \(A O C = \alpha\) radians. \(A C\) and \(B D\) are arcs of circles, centre \(O\) and radii 10 cm and 16 cm respectively.
  1. In the case where \(\alpha = 0.8\), find the area of the shaded region.
  2. Find the value of \(\alpha\) for which the perimeter of the shaded region is 28.9 cm .