Question

In figure, in a circle with center O, the length of chord AB is equal to the radius of the circle. Find the measure of the following.

(i) ∠AOB

(ii) ∠ACB

(iii) arc AB.

Answer 1

(i) seg OA = seg OB = radius   ...(i) [Radii of the same circle]

seg AB = radius                        ...(ii) [Given]

∴ seg OA = seg OB = seg AB   ......[From (i) and (ii)]

∴ ∆OAB is an equilateral triangle.

∴ m∠AOB = 60°   ...[Angle of an equilateral triangle]

(ii) m∠ACB = `1/2` m∠AOB     ...[Measure of an angle subtended by an arc at a point on the circle is half of the measure of the angle subtended by the arc at the centre]

∴ m∠ACB = `1/2 xx 60^circ`

∴ m∠ACB = 30°

(iii) m(arc AB) = m∠AOB   ...[Definition of measure of minor arc]

∴ m(arc AB) = 60°