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\includegraphics[max width=\textwidth, alt={}, center]{097c5d00-9f92-4c3e-8056-7de09347fbb6-10_716_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 \(r\).