AB is a common tangent to both the circles in the given figure. Find the distance (correct to two decimal places) between the centres of the two circles.

Solution (By Examveda Team)

$$\eqalign{ & \Rightarrow {\text{By figure,}} \cr & \Delta CAE \sim \Delta DBE \cr & \frac{{CA}}{{BD}} = \frac{{AE}}{{BE}} \cr & \frac{5}{x} = \frac{8}{{12}} \cr & x = 7.5 = \left( {\frac{{15}}{2}} \right) \cr & \Rightarrow {\text{Length of T}}{\text{.L}} = \sqrt {{d^2} - {{\left( {{R_1} + {R_2}} \right)}^2}} \cr & {\left( {20} \right)^2} = {d^2} - {\left( {5 + 7.5} \right)^2} \cr & 400 = {d^2} - 156.25 \cr & {d^2} = 400 + 156.25 \cr & {d^2} = 556.25 \cr & d = \sqrt {556.25} \cr & d = 23.58 \cr} $$