Question

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

• A. 2
• B. 4
• C. 8
• D. 16

Answer 1

Answer: (B)

Length of the chord
$=\sqrt{{\left[4\cos \left(\theta +60^{\circ }\right)-4\cos \theta \right]}^2}+{\left[4\sin \left(\theta +60^{\circ }\right)-4\sin \theta \right]}^2$
$4\sqrt{co{s}^2\left(\theta +60^{\circ }\right)+co{s}^2\theta +si{n}^2\left(\theta +60^{\circ }\right)+si{n}^2\theta -2cos\left(\theta +60^{\circ }\right)cos\theta -2sin\left(\theta +60^{\circ }\right)sin\theta }$
$=4\sqrt{1+1-2\cos 60^{\circ }}=4$