In the diagram, $$$\operatorname{arc} A B$$$ is part of a circle with centre $$$O$$$ and radius $$$8 \mathrm{~cm}$$$. Arc $$$B C$$$ is part of a circle with centre $$$A$$$ and radius $$$12 \mathrm{~cm}$$$, where $$$A O C$$$ is a straight line. Find the area of the shaded region. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w20_qp_13 Year：2020 Question No：9(b)

Answer:

Sector $A B C=1 / 2 \times 12^{2} \times$ their $0.7227$
Triangle $A O B=1 / 2 \times 8 \times 12 \sin ($ their $0.7227)$ or $1 / 2 \times 12 \times \sqrt{2} 8$
Shaded area $=$ their $52.0-$ their $31.7=20.3$

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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