SSC CGL 2022 PYQ — Question 56

The correct answer is option 1 i.e. 38 cm

Given:

The radii of two concentric circles with centre O are 26 cm and 16 cm.

Chord AB of the larger circle is tangent to the smaller circle at C and AD is a diameter.

Calculations:

According to the question we have

OA = OD = 26 cm

OC is the radius of smaller cirlce = 16 cm

DB || OC (line divides any two sides in the same ratio then the line is parallel to the third line)

BD = 2 × OC = 32 cm

Using pythagoras theorem in triangle AOC,

⇒ OA² = OC² + AC²

⇒ 26² = 16² + AC²

⇒ AC = 676 - 256

⇒ AC = BC = √420

Now using pythagoras theorem again in triangle BCD

⇒ CD² = BD² + BC²

⇒ CD² = 32² + (√420)²

⇒ CD² = 1024 + 420 = 1444

⇒ CD = 32 cm