In the diagram, $$$O A B$$$ is a sector of a circle with centre $$$O$$$ and radius $$$2 r$$$, and angle $$$A O B=\frac{1}{6} \pi$$$ radians. The point $$$C$$$ is the midpoint of $$$O A$$$. Find the exact area of the shaded region. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_12 Year：2020 Question No：7(c)

Answer:

Area $=$ sector $-$ triangle
Sector area $=\frac{1}{2} 4 r^{2} \frac{\pi}{6}$
Triangle area $=1 / 2 r .2 r \sin \frac{\pi}{6}$
Shaded area $=r^{2}\left(\frac{\pi}{3}-\frac{1}{2}\right)$

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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