SSC CGL 2023 PYQ — Question 52

The correct answer is option 4 i.e.  $8\sqrt{6}$ cm.

According to the given question,

If two circles touch externally, the length of common tangent can be calculated by using the formula,

Common tangent = $2\sqrt{r_1r_2}$

Where r₁ and r₂ are the radius of two circles

Given that, r₁ = 12 cm

And r₂ = 8 cm

Now, in the above figure,

Common tangent = $2\sqrt{r_1r_2}$

⇒ $2\sqrt{12 \times 8}$

⇒ $2\sqrt{96}$

⇒ $2\sqrt{16 \times 6}$

⇒ $8\sqrt{ 6}$ cm

Hence the length of common tangent is $8\sqrt{ 6}$ cm.