Q. 64.3( 7 Votes )

In Fig. 10.6, if OAB = 40 �, then ACB is equal to:


A. 50 �

B. 40 �

C. 60 �

D. 70°

Answer :

In triangle AOB,

AO = OB = Radius


OAB = OBA = 40° ( angles opposite to equal sides are equal)


Using the angle sum property of triangle, sum of all angles of a triangle is 180°,


OAB + OBA + AOB = 180°


40° + 40° + AOB = 180°


AOB = 180° - 40° - 40°


AOB = 100°


By theorem “The angle subtended by an arc at the center of a circle is twice the angle subtended by it at remaining part of the circle”, we have:


AOB = 2 × ACB


ACB = AOB/2


= 100°/2


ACB = 50°

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