Question

A chord of a circle of radius 6cm is making an angle 60° at the centre. Find the length of the chord.​

Answer 1

IN TRIANGLE AOB, AO=BO=6cm

THEREFORE,∠OAB=∠OBA=y(say)

IN TRIANGLE AOB BY ANGLE SUM PROPERTY

60°+y+y=180°⇒180°-60°=2y⇒120°=2y⇒y=60°

THEREFORE AS ∠A=∠B=∠C=60°

THEREFORE TRIANGLE AOB IS AN EQUILATERAL TRIANGLE

⇒LENGTH OF CHORD AB =6cm.

Answer 2

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A chord of a circle of radius 6cm is making an angle 60° at the centre. Find the length of the chord.

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Given the radius of the circle

OA = OB = 6cm, ∠AOB = 60°

OC is height from 'O' upon AB and it is an angle bisector.

Then, ∠COB = 30°

Consider ∆COB

sin 30° = BC / OB

1/2 = BC/6

BC = 6/2 = 3

But, length of the chord AB = 2BC

= 2 × 3

= 6 cm

∴ Length of the chord = 6 cm

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