A chord AB of a circle subtends an angle of 30° at its circumference. Then the radius of the circle is

Concept:

An angle subtended by the chord at the center of the circle is twice the angle subtended at the circumference of the circle. 

From the figure: ∠O = 2∠C.

Explanation:

Let, ∠C = 30^o 

As per the above statement, the angle subtended at the center will be twice the angle at C.

Hence, ∠O = 60^o 

Now, the triangle AOB will be an equilateral triangle as all angles are 60^o. Hence, all the side will be equal.

∴ AO = OB = AB

So, the radius of the The radius of the circle is equal to the length of the chord AB.