SSC CHSL 2023 PYQ — Question 57

The correct answer is option 4 i.e.  $6\sqrt{30}$.

Given that

Two circles of radii 15 and 18 cm touch each other externally

Big circle radii R = 18 cm

Small circle radii r = 15 cm

Distance between centers of circles D = R + r = 18 + 15 = 33 cm

Formula used

Direct common tangent = √(D² - (R - r)²)

where, D = the distance between the centers of the circles

Calculation

DCT = √(33² - (18 - 15)²)

DCT = √(1089 - 3²) = √1080 =  $6\sqrt{30}$