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Question

In the figure, if AOB is a diameter of the circle and AC = BC, then CAB is equal to

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Solution

We know that, diameter subtends a right angle to the circle.
BCA=90(i)Given,AC=BCABC=CAB(ii) [angle opposite to equal sides are equal]In ΔABC,CAB+ABC+BCA=180 [by angle sum property of a triangle]CAB+ABC+BCA=180[from Eqs.(i) and (ii)]2CAB=18090CAB=902CAB=45

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