Question

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

1. ∠AOB
2. ∠ACB
3. 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°