The diagram shows a sector OAB of a circle with centre O and radius r. Angle AOB

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The diagram shows a sector OAB of a circle with centre O and radius r. Angle AOB is θ radians. The point C on OA is such that BC is perpendicular to OA. The point D is on BC and the circular arc AD has centre C.


i. Find AC in terms of r and θ.
ii. Find the perimeter of the shaded region ABD when


giving your answer as an exact value.

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