SSC CHSL 2023 PYQ — Question 53

The correct answer is Option 2 i.e. $2\sqrt{3}$.

We know that tangents drawn from an external point are equally inclined to the line joining that point to the center

⇒ ∠APO = ∠BPO = ∠APB/2 = 120/2 = 60°

Now In ΔΟΑΡ

⇒ ∠OAP = 90° (Tangent is perpendicular to the radius at the point of contact)

Now in the right ΔOAP

⇒ ∠OPA = 60°

⇒ tan 60° = OA/AP

From the trigonometric table tan 60° = √3

⇒ √3 = 6/AP

⇒ AP = 6/√3 = 2√3

Also, tangents drawn from an external point are equal in length

⇒ AP = PB = 2√3