A-LevelMathematicsCircular measure9709/12 · Feb/Mar 2022 · Q108 Marks
The diagram shows a circle with centre A of radius 5cm and a circle with centre B of radius 8cm. The circles touch at the point C so that ACB is a straight line. The tangent at the point D on the smaller circle intersects the larger circle at E and passes through B. [Figure 10.1]
- (a)Find the perimeter of the shaded region.[5]
- (b)Find the area of the shaded region.[3]
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Mark scheme
Marking points from the official mark scheme (Feb/Mar 2022). The mark or mark type is shown in brackets.
- [M1] tan A = 12/5 or cos A = 5/13 or sin A = 12/13
- [A1] A = 1.176 B = 0.3948
- [B1] DE = 4
- [M1] Arcs = 5xtheir1.176 and 8×their0.3948
- [A1] [Perimeter = 5.880 +3.158 + 4 =] 13.0
- [B1 FT] Area of triangle = ½ × 5 × their12 [ = 30]
- [M1] Area of sectors = ½×5²×their 1.176+½×8²×their 0.3948
- [A1] [Area = 30-14.70 -12.63 =] 2.67
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