The lengths of radii of two circles are 8cm and 3 cm and distance between two centre is 13 cm. let us find the length of a common tangent of two circles.
A and B are the centre of the two circles
CD is the common tangent
Radius of circle A = 8 cm
Radius of circle B = 3 cm
AB = 13 cm
Since ED∥ AB so
ED = 13 cm
EC = (8-3) = 5cm
Applying Pythagoras theorem in Δ CED we get
Length of tangent = √(132-52)
⇒ Length of tangent = √ 144 = 12 cm
12