SSC CHSL 2024 PYQ — Question 60

The correct answer is Option 4 i.e. $4{\sqrt{34}}$ cm.

Given: RS = 20 cm, PQ = 12 cm

So, AR = 20/2 = 10 cm,

PQ = 12/2 = 6 cm

Now,

In △ORA

⇒ OR² = AR² + OA²

⇒ OR² = 10² + OA².....(1)

In △OPB

⇒ OP² = BP² + (OA + 4)²....(2)

here, OR = OP are radius

So, OR² = OP²

⇒ 10² + OA² + 6² + (OA + 4)²

⇒ 100 + OA² = 36 + OA² + 16 + 8 × OA

⇒ 100 = 52 + 8 × OA

⇒ 8 × OA = 48

⇒ OA = 48/8 = 6 cm

Putting OA in equation 1

⇒ OR² = 100 + 6²

⇒ OR² = 100 + 36 = 136

⇒ OR² = √136 = 2√34 cm

Hence, diameter(2 × OR) = 2 × 2√34 = 4√34 cm