CAIE P1 2010 November — Question 8

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2010
SessionNovember
TopicCircles

8
\includegraphics[max width=\textwidth, alt={}, center]{32a57386-2696-4fda-a3cb-ca0c5c3be432-3_600_883_1731_630} The diagram shows a rhombus \(A B C D\). Points \(P\) and \(Q\) lie on the diagonal \(A C\) such that \(B P D\) is an arc of a circle with centre \(C\) and \(B Q D\) is an arc of a circle with centre \(A\). Each side of the rhombus has length 5 cm and angle \(B A D = 1.2\) radians.
  1. Find the area of the shaded region \(B P D Q\).
  2. Find the length of \(P Q\).