SSC CGL 2023 PYQ — Question 60

The correct answer is option 3 i.e. 15.82 cm.

AB = 28 cm and CD = 22 cm, EF = 4 cm, OA = OC = r

AE = $28 \over 2$ = 14 cm, CF = $22 \over2$ = 11 cm

In the triangle $\triangle$OCF and $\triangle$OAE

OC² = OF² + CF²

⇒ r² = (OE + 4)² + 11²     .....................(1)

OA² = OE² + AE²

⇒ r² = OE² + 14²     .....................(2)

From equation 1 and 2

⇒ OE² + 14² = (OE + 4)² + 11²

⇒ OE² + 196 = OE² + 16 + 8OE + 121

⇒ 8OE = 196 - 137 = 59

⇒ OE =$59 \over 8$

Hence, the radius = $\sqrt{14^2+({59\over 8})^2 }$ = 15.82 cm