2.7: Lens-shaped region from overlapping circles

0606/22/M/J/20 — Question 11 · 8 marks

2.7 diagram
The circles with centres C1C_{1} and C2C_{2} have equal radii of length r cmr\text{ cm}. The line C1C2C_{1}C_{2} is a radius of both circles. The two circles intersect at AA and BB.
(a)
Given that the perimeter of the shaded region is 4π cm4\pi\text{ cm}, find the value of rr.
[4]
(b)
Find the exact area of the shaded region.
[4]