Q15 of 63 Page 156

In figure, if AOB is a diameter of a circle and AC = BC. Then ∠CAB is equal to—

Given AOB is a diameter of a circle and AC = BC.


We know that diameter subtends a right angle to the circle.


∴ ∠BCA = 90°


We know that angles opposite to equal sides are equal.


∴ ∠ABC = ∠CAB


In ΔABC,


By angle sum property,


⇒∠CAB + ∠ABC + ∠BCA = 180°


⇒∠CAB + ∠CAB + 90° = 180°


⇒ 2 ∠CAB + 90° = 180°


⇒ 2 ∠CAB = 180° - 90°


⇒∠CAB = 90°/ 2


∴ ∠CAB = 45°

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