Q. 105.0( 1 Vote )

# Find the length of the chord of a circle of radius 5cm subtending an angle of 108° at the centre.

Answer :

Let AB be the chord of a circle of radius 5 cm with O as centre.

Draw OC perpendicular to AB.

∴ C is the midpoint of AB and ∠AOB = 108°

Then ∠AOC = = 54°

In right angled triangle OCA,

⇒ sin 54° =

⇒ sin 54° =

⇒ AC = sin 54° × 5

= 0.8090 × 5

= 4.045 cm

∴ Length of the chord AB = AC × 2 = 4.045 × 2 = 8.90 cm

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