SSC CGL 2021 PYQ — Question 58

The correct answer is option 3 i.e. 3$\sqrt{13}$.

OA is perpendicular to AB and OX is perpendicular to CD.

OB = OD = radius.

In triangle OBY,

OB² = OY² + 6²

OB² = OY² + 36......(1)

In triangle ODX,

⇒ OD² - OX² + 9²

⇒ OD² = OX² + 81...(2)

From Equation (1) and (2) we get,

⇒  OX² + 81 = OY² + 36

⇒  81 -  36 = OY² - OX² 

⇒ 45 = (OY + OX)(OY - OX)

Here OY + OX = 15...........(3)

So one can say that OY - OX = 3.......(4)

From equation 3 and 4 we get,

OX = 6 cm and OY = 9.

⇒ OB² = OY² + 36

⇒ OB² = 81 + 36 = 117

⇒ OB =  3$\sqrt{13}$.