SSC CGL 2022 PYQ — Question 52

 The correct answer is option 1 i.e. $8\sqrt 3 \;{\mathop{\rm cm}\nolimits}$

Concept used:

Pythagoras theorem

Calculation:

In the following figure, we have

OA = r, OO' = r

AM is perpendicular to OO'

Hence, OM = O'M = r/2

Common tangent = AB = 2AM

Using pythagoras theorem, we get

⇒ AM² = OA² - OM²

⇒ AM² = r² - (r/2)²

⇒ AM² = r² - r²/4

⇒ AM² = 3r²/4

⇒ AM = √3r/2

Now, AB = 2 × √3r/2 = √3r

We have the value of radius i.e. r = 8 cm

Theorefore, the length of the common tangent = 8√3 cm