Radii of two circles are 20 cm and 4 cm. Length of direct common tangent is 30 cm. What is the distance between their centres?

34 cm

Let the distance between their centers be x cm.

According to the formula,

= 30 = \(\sqrt {(x^2 - (20 - 4)^2) }\)

= 30 = \(\sqrt {(x^2 - (16)^2) }\)

= 900 = x^2 - 256

= x^2 = 900 + 256 = 1156

= x = 34

Therefore, distance between them is 34 cm.