Question

The length of the chord joining the points $(4\cos \theta ,4\sin \theta )$ and $\left(4\cos \right(\theta +{60}^o\left)\right)$ ,
$\left(4\sin \right(\theta +{60}^o\left)\right)$ of the circle $x^2+y^2=16$ is

• A. $16$
• B. $2$
• C. $8$
• D. $4$

Answer 1

The correct option is D $4$

The points are given in the parametric form and subtend ${60}^o$ angle at the centre.

If $r$ is the radius of the circle, then the length of the chord joining these points is $2r\sin {30}^o=r$.

The radius of $x^2+y^2=16$ is $4$ so the length of the chord is $4$.

So option D is the correct answer.