A triangle ABC is made on a circle, where AB is the…

A triangle ABC is made on a circle, where AB is the diameter of the circle. If BC is equal to the radius of the circle and ∠ABC = x ∠BAC, then x is :

Show answer & explanation

Correct answer: B

Explanation

The correct answer is Option 2 i.e. 2.

In △ABC

⇒ AB² = AC² + BC²

⇒ (2r)² = AC² + r²

⇒ 4r² = AC² + r²

⇒ AC² = 3r²

⇒ AC = $\sqrt{3} r$

Now,

⇒ sin∠BAC = BC/AB = r/2r = 1/2

⇒ sin∠BAC = sin 30°

⇒ ∠BAC = 30°

Since ∠ACB = 90°,

⇒ ∠ACB = 90° - 30° = 60°

So,

⇒ ∠ABC = x × ∠BAC

⇒ 60° = x × 30°

⇒ x = 60°/30°

⇒ x = 2

SSC CGL 2024 PYQ — Question 72