SSC CPO 2022 PYQ — Question 106

The correct answer is Option 2 i.e. ${3\sqrt3} \;cm$.

Let PQ and PR be the tangents drawn to a circle

Now, according to the question

⇒ √RPQ = 60°

So, QP = RP

in △PQO and △PRO

⇒ QP = RP

⇒ QO = RO [radius]

⇒ PO = PO [common side]

△PQO and △PRO are similar by SSS criterion

At the point of contact, the radius of a circle is perpendicular to the tangent

So, √PQO = √PRO = 90°

Since, QO = RO = radius

⇒ √PQO = √PRO

⇒ √RPO = √PQO + √PRO

⇒ 2√PQO = 60°

⇒ √PQO = 60°/2 = 30°

In △PQO

PQO is a right triangle with A at right angle

⇒ tan 30° = QO/PQ

⇒ 1/√3 = 3/QP

⇒ QP = 3√3 cm

Thus, the length of each tangent is 3√3 cm