SSC CGL 2024 PYQ — Question 74

The correct answer is option 4 i.e.  $\sqrt{19}$ cm.

The product of one whole secant segment and its external segment is equal to the product of the other whole secant segment and its external segment.

OP = 17 cm, PA = 12 cm and PB = 22.5 cm

Here, OD = OC = r cm (Radius)

So, PA × PB = PC × PD

⇒ PA × PB = (OP - OC)(OP + OD)

⇒ 12 × 22.5 = (17 - r)(17 + r) = 17² - r²

⇒ 270 = 289 - r²

⇒ r² = 289 - 270 = 19

⇒ r = √19

Therefore, the radius of the circle is √19 cm.