Question

The angle between a pair of tangents from a point $P$ to the circle $x^2+y^2=16$ is $\frac{\pi }{3}$ and locus of $P$ is $x^2+y^2=r^2$, then value of $r$ is

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Answer 1

The correct option is D $8$

REF.Image

$x^2+y^2=16$, $\theta =\frac{\pi }{3}$

Now, $AO=4$

$\therefore PO=8$

Now, locus of P would be a circle

with centre at O and

radius PO = 8

$\therefore x^2+y^2=8^2$

$\therefore r=8$