SSC CHSL 2023 PYQ — Question 65

The correct answer is Option 1. i.e.  $\frac{\sqrt265}{4}$.

Given that

AB = 8 cm and CD = 6 cm are two parallel chords on the same side of the center of a circle

the distance between them PQ = 2 cm

According to the question

AP = AB/2 = 8/2 = 4 cm

CQ = CD/2 = 6/2 = 3 cm

In triangle AOP,

OA² = OP² + AP²

⇒ r² = OP² + 16 .....(1

Similarly, 

In triangle OCQ,

OC² = OQ² + CQ²

⇒ r² = (OP + 2)² + 9 

Equation 1 = Equation 2

⇒ OP² + 16 = (OP + 2)² + 9 = OP² + 4 + 4OP + 9 

⇒ 4OP = 16 - 13 = 3

⇒ OP = 3/4

Hence, r² = OP² + 16 = (3/4)² + 16 = 9/16 + 16 

r = $\frac{\sqrt265}{4}$ cm