Challenging +1.2 This is a multi-step geometry problem requiring calculation of lengths using trigonometry, then finding areas of two circular sectors and subtracting triangular areas. While it involves several steps and careful geometric reasoning, the techniques are all standard (right-angled trigonometry, sector area formula) with no novel insight required. The main challenge is careful bookkeeping across multiple steps, making it moderately above average difficulty.
9
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The diagram shows a triangle \(O A B\) in which angle \(A B O\) is a right angle, angle \(A O B = \frac { 1 } { 5 } \pi\) radians and \(A B = 5 \mathrm {~cm}\). The arc \(B C\) is part of a circle with centre \(A\) and meets \(O A\) at \(C\). The arc \(C D\) is part of a circle with centre \(O\) and meets \(O B\) at \(D\). Find the area of the shaded region.
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\includegraphics[max width=\textwidth, alt={}, center]{d178603a-f59a-4986-b5ab-b47eceedb2fc-14_465_677_260_733}
The diagram shows a triangle $O A B$ in which angle $A B O$ is a right angle, angle $A O B = \frac { 1 } { 5 } \pi$ radians and $A B = 5 \mathrm {~cm}$. The arc $B C$ is part of a circle with centre $A$ and meets $O A$ at $C$. The arc $C D$ is part of a circle with centre $O$ and meets $O B$ at $D$. Find the area of the shaded region.\\
\hfill \mbox{\textit{CAIE P1 2018 Q9 [8]}}