SSC CHSL 2024 PYQ — Question 71

The correct answer is Option 2 i.e. $36 \sqrt5$.

We know that,

The length of common tangent(L) = √(d² - (r₁ - r₂)²)

here, d = distance between the centers

r₁ and r₂ = radii of the circles

So,

⇒ L = √(d² - (r₁ - r₂)²)

⇒ L = √(81² - (51 - 42)²)

⇒ L = √(81² - 9²)

⇒ L = √(6561 - 80)

⇒ L = √6481

⇒ L = $36 \sqrt5$ cm 

Thus, The length of the direct common tangent is $36 \sqrt5$ cm