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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.
Solution
(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°
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