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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