Test Index

NDA Math Circle

© examsnet.com

Question : 7 of 26

Marks: +1, -0

A chord subtends an angle

120^{\circ}

at the centre of a unit circle. What is the length of the chord?

$\sqrt{2}-1$ units
$\sqrt{3}-1$ units
$\sqrt{2}$ units
$\sqrt{3}$ units

Solution: 👈: Video Solution

Concept:

Length of chord

=2 r \sin \left( \frac{\theta}{2} \right)

Where

r

is the radius of the circle and

\theta

is the angle from the center of the circle to the two points of the chord.

Calculation:

Given:

r=1

and angle

=120^{\circ}

Now, Length of chord

\;\;=2(1)\sin\left( \frac{120^{\circ}}{2} \right)

\;\; =2 \sin(60^{\circ})

\;\; =2 \times \frac{\sqrt{3}}{2}

\;\; =\sqrt{3} \; \text{ units } \;

© examsnet.com

Go to Question:

Prev Question

Next Question