2.8: Major segment of a circle

0606/23/M/J/17 — Question 8 · 8 marks

2.8 diagram
The diagram shows a circle, centre OO of radius r cmr\text{ cm}, and a chord ABAB. Angle AOB=θAOB = \theta radians. The length of the major arc ABAB is 55 times the length of the minor arc ABAB. The minor arc ABAB has length 2π cm2\pi\text{ cm}.
(i)
Find the value of θ\theta and of rr.
[2]
(ii)
Calculate the exact perimeter of the shaded segment.
[2]
(iii)
Calculate the exact area of the shaded segment.
[4]