The diagram shows a sector $$$C A B$$$ which is part of a circle with centre $$$C$$$. A circle with centre $$$O$$$ and radius $$$r$$$ lies within the sector and touches it at $$$D, E$$$ and $$$F$$$, where $$$C O D$$$ is a straight line and angle $$$A C D$$$ is $$$\theta$$$ radians. It is now given that $$$r=4$$$ and $$$\theta=\frac{1}{6} \pi$$$. Find the perimeter of sector $$$C A B$$$ in terms of $$$\pi$$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w20_qp_11 Year：2020 Question No：10(b)

Answer:

Radius of $\operatorname{arc} A B=4+\frac{4}{\sin \frac{\pi}{6}}=4+8=12$
(Arc $A B=$ ) their $12 \times \frac{2 \pi}{6}$ or $\left(\frac{1}{2} A B=\right)\left(\right.$ their $\left.12 \times \frac{\pi}{6}\right)$
Perimeter $=24+4 \pi$

Knowledge points:

1.4.2 use the formulae in solving problems concerning the arc length and sector area of a circle (Including calculation of lengths and angles in triangles and areas of triangles.)

Answer:

Knowledge points:

Solution:

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