Q10 of 164 Page 50

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


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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