SSC CGL 2024 PYQ — Question 51

The correct answer is option 4 i.e. 48.

According to the given question,

Let the tangent from T meets the circle at P, O be the center of the circle and r be the radius of the circle.

The line from the center of the circle to the point where tangent meets the circle makes as angle of 90° with the tangent.

Now, in the above figure, in triangle OPT, ∠OPT is a right angle.

Applying Pythagoras theorem in triangle OPT,

OP² + PT² = OT²

⇒ r² + 32² = 40² 

⇒ r² + 1024 = 1600

⇒ r² = 576

⇒ r = 24

Now, diameter = 2r

⇒ 2 × 24 = 48

Hence the diameter (in cm) of the circle is 48.