If a chord of a circle subtends an angle of 30° at the circumference of the circle, then what is the ratio of the radius of the circle and the length of the chord respectively?

Given : $$\angle$$ ACB = 30°

To find : OA : AB = ?

Solution : Angle subtended by an arc at the centre is double the angle subtended by it at any point on the circle.

=> $$\angle$$ AOB = $$2\times$$ $$\angle$$ ACB

=> $$\angle$$ AOB = $$2\times30^\circ=60^\circ$$

In $$\triangle$$ AOB, OA = OB = radii of circle

=> $$\angle$$ OAB = $$\angle$$ OBA = $$60^\circ$$

Thus, $$\triangle$$ OAB is an equilateral triangle and OA = OB = AB

=> OA : AB = 1 : 1

=> Ans - (A)