In figure 3.56, in a circle with centre O, length of chord AB is equal to the radius of the circle. Find measure of each of the following.

(1) AOB
(3) arc AB
(4) arc ACB.


(1)OA and OB are the radius of circle.
Given AB = radius of circle
AB = OA = OB
OAB is an equilateral triangle.
AOB = 60˚ [Angle of equilateral triangle = 60˚]
(2)ACB = ½ AOB [The 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.]
ACB = ½ ×60 = 30˚
(3)arc AB = AOB [Measure of a minor arc is equal to the measure of its corresponding central angle.]
arc AB = 60˚
(4)m(arc AB) + m(arc ACB) = 360˚ [Measure of a complete circle is 360°]
60+ m(arc ACB) = 360˚
m(arc ACB) = 360-60 = 300˚
Hence arc(ACB ) = 300˚

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