The diagram shows a sector $$\(C A B\)$$ which is part of a circle with centre $$\(C\)$$. A circle with centre $$\(O\)$$ and radius $$\(r\)$$ lies within the sector and touches it at $$\(D, E\)$$ and $$\(F\)$$, where $$\(C O D\)$$ is a straight line and angle $$\(A C D\)$$ is $$\(\theta\)$$ radians. Find $$\(C D\)$$ in terms of $$\(r\)$$ and $$\(\sin \theta\)$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

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