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\includegraphics[max width=\textwidth, alt={}, center]{518bb805-5b14-4b41-94fd-38a31a90c218-06_401_698_255_721}
The diagram shows a semicircle with centre \(O\) and radius 6 cm . The radius \(O C\) is perpendicular to the diameter \(A B\). The point \(D\) lies on \(A B\), and \(D C\) is an arc of a circle with centre \(B\).
- Calculate the length of the \(\operatorname { arc } D C\).
- Find the value of
\(\frac { \text { area of region } P } { \text { area of region } Q }\),
giving your answer correct to 3 significant figures.