The radius of two circles is 3 cm and 4 cm. The distance between the centres of the circles is 10 cm. What is the ratio of the length of direct common tangent to the length of the transverse common tangent?

Solution (By Examveda Team)

Direct common tangent:
Transverse common tangent
$$\eqalign{ & \sqrt {{D^2} - {{\left( {{r_1} - {r_2}} \right)}^2}} :\sqrt {{D^2} - {{\left( {{r_1} + {r_2}} \right)}^2}} \cr & \sqrt {{{10}^2} - {{\left( {4 - 3} \right)}^2}} :\sqrt {{{10}^2} - {{\left( {4 + 3} \right)}^2}} \cr & \sqrt {99} :\sqrt {51} \cr & \sqrt {33} :\sqrt {17} \cr} $$