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\includegraphics[max width=\textwidth, alt={}, center]{a9e04003-1e43-40c4-991a-36aa3a93654b-3_718_899_258_621}
The diagram shows a circle with centre \(A\) and radius \(r\). Diameters \(C A D\) and \(B A E\) are perpendicular to each other. A larger circle has centre \(B\) and passes through \(C\) and \(D\).
- Show that the radius of the larger circle is \(r \sqrt { } 2\).
- Find the area of the shaded region in terms of \(r\).