If two circles of radius 6 cm and 2 cm have their centers…

If two circles of radius 6 cm and 2 cm have their centers 10 cm apart, what is the length of the direct common tangent?

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. 2 $\sqrt{21}$ cm.

Radii r₁ = 6 cm, r₂ = 2 cm

Distance between center (d) = 10 cm

Direct common tangent length $= \sqrt{d^2 - (r₁ - r₂)^2}$

$= \sqrt{100 - (6-2)^2}$

$=\sqrt{100-4^2}$

$= \sqrt{100 - 16}$

$= \sqrt{84}$

$= 2\sqrt{21}$ cm

SSC CGL 2025 PYQ — Question 55