The chord of a circle is 3 times its radius The angle subtended by this chord at the minor arc is k ...........

Quantitative Aptitude (CDS) Mensuration 2D

The chord of a circle is 3 times its radius. The angle subtended by this chord at the minor arc is k times the angle subtended at the major arc. What is the value of k?

1/2

1/5

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Explanation:

Let radius be r

AB= $\small \sqrt{3r}$

$\small BL=\frac{\sqrt{3}}{2}r$
$\small In\; \Delta OLB,$
$\small \frac{LB}{OB}=sin(\frac{\Theta }{2})$

$\small \frac{r\sqrt{3}}{2r}=sin(\frac{\Theta }{2})$

$\small sin(\frac{\Theta }{2})=sin(60^{o})$
$\small \frac{\Theta }{2}=60$
$\small \Theta$ =60*2=120^o
Minor angle = 120
Major angle = 360 - 120 = 240 = 2 x 120
Thus, k = 2