SSC CHSL 2024 PYQ — Question 70

The correct answer is option 4 i.e. $6\sqrt{2}$.

Let the radii of the two circles be:

Radius of circle O: r$_1$= 6 cm

Radius of circle A: $r_2$ = 3 cm

The two circles touch each other externally, meaning the distance between their centers, OA is the sum of their radii:

OA = $r_1 + r_2$ = 6 + 3 = 9 cm.

The length L of the common external tangent between two circles is given by the formula:

$L = \sqrt{d^2 - (r_1 - r_2)^2}$

where d is the distance between the centers of the circles, and  r$_1$​ and $r_2$​ are the radii of the two circles.

In our case:

d= 9 cm (the distance between the centers O and A),

 r$_1$​ = 6 cm,

$r_2$= 3 cm.

Now, substitute the values into the formula for L:

$L= \sqrt{9^2 - (6 - 3)^2} = \sqrt{81 - 9} = \sqrt{72}$

Simplifying $\sqrt{72}$​:

$L=\sqrt{36 \times 2} = 6\sqrt{2}​$