(Q9)A chord of a circle of radius 6cm is making an angle 60° at the centre. Find the length of the chord

ABCO6cm6cm

Given that the radius of the circle is OA = OB = cm and

∠AOB = 60°

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

Then, ∠COB = 30°.

Consider △COB

sin 30° =
BC
1
 =
BC
BC =
= .

But, length of the chord AB = 2BC

= 2 × = cm

Therefore, length of the chord = cm.