O-LevelAdditional MathematicsCircular measure4037/22 · May/June 2020 · Q118 Marks
The circles with centres C₁ and C₂ have equal radii of length r cm. The line C₁C₂ is a radius of both circles. The two circles intersect at A and B. [Figure 11.1]
- (a)Given that the perimeter of the shaded region is 4π cm, find the value of r.[4]
- (b)Find the exact area of the shaded region.[4]
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Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [2] (a) [perimeter =] (4/3)πr soi
- [1] (a) (their (4/3)πr) = 4π oe
- [1] (a) r=3
- [1] (b) 1/2 × their3² × their (2π/3) oe
- [1] (b) 1/2 × their3² × sin their (2π/3) oe
- [1] (b) For subtracting and doubling: their3² × their (2π/3) - their3² sin their (2π/3)
- [1] (b) 6π - (9/2)√3 or exact equivalent
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