In the given figure, BOC is a diameter of a circle and AB = AC. Then, ∠ABC = ?

Question:

In the given figure, BOC is a diameter of a circle and AB = AC. Then, ABC = ?
(a) 30°
(b) 45°
(c) 60°
(d) 90°

Solution:

(b) 45°

Since an angle in a semicircle is a right angle, ∠BAC = 90°
∴ ∠ABC + ∠ACB = 90°

Now, AB = AC       (Given)
⇒ ∠ABC = ∠ACB = 45°

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