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 $$$O A$$$. Show that the exact length of $$$B C$$$ is $$$r \sqrt{5-2 \sqrt{3}}$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

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

Answer:

$B C^{2}=r^{2}+4 r^{2}-2 r .2 r \times \cos \left(\frac{\pi}{6}\right)=5 r^{2}-2 r^{2} \sqrt{3}$
$B C=r \sqrt{(5-2 \sqrt{3})}$

1.5.2 use the exact values of the sine, cosine and tangent of 30°, 45°, 60°, and related angles