Question

A chord of a circle subtends an angle of 120° at the Centre of a circle of radius 21cm, find the length of the chord.

A) 21√3 cm
B) 42 cm
C) 21 cm
D) 42√3 cm

Answer 1

To find the length of a chord in a circle, use the formula: length of chord = 2 x radius x sin(angle/2). In this case, the length of the chord is 21√6 cm.

Step-by-step explanation:

To find the length of the chord, we need to use the formula: length of chord = 2 x radius x sin(angle/2).

Given that the radius of the circle is 21 cm and the angle at the center is 120°, we can calculate the length of the chord as follows:

length of chord = 2 x 21 cm x sin(120°/2)

Using the formula for the sin of half an angle, sin(A/2) = √[(1 - cos(A))/2]:

length of chord = 2 x 21 cm x √[(1 - cos(120°))/2]

Since cos(120°) = -1/2:

length of chord = 2 x 21 cm x √[(1 - (-1/2))/2]

length of chord = 2 x 21 cm x √[(1 + 1/2)/2]

length of chord = 2 x 21 cm x √(3/2)

Simplifying the expression:

length of chord = 2 x 21 cm x √3/√2

length of chord = 2 x 21 cm x (√3/√2) x (√2/√2)

length of chord = 2 x 21 cm x (√6/2)

length of chord = 42 cm x (√6/2)

length of chord = 21√6 cm