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
$=\sqrt{\left[4 \cos \left(\theta+60^{\circ}\right)-4 \cos \theta\right]^{2}}{+\left[4 \sin \left(\theta+60^{\circ}\right)-4 \sin \theta\right]^{2}}$
$4\sqrt{cos^{2}\,\left(\theta +60^{\circ}\right)+cos^{2}\,\theta +sin^{2} \,\left(\theta +60^{\circ}\right)+sin^{2}\,\theta-2\, cos\, \left(\theta +60^{\circ}\right)\,cos \,\theta -2 \,sin \left(\theta +60^{\circ}\right) \,sin \,\theta}$
$=4 \sqrt{1+1-2 \cos 60^{\circ}}=4$