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

$\sqrt{33}:\sqrt{17}$

Radius of first circle , r1 = 3 cm

Radius of 2nd circle , r2 = 4 cm

Distance between the centers = 10 cm

Length of Direct common tangent  :   Length of Transverse common tangent

\(\sqrt {d² - ( r2 - r1)² }\)  :  \(\sqrt { d² - ( r2 + r1)² }\)  

\(\sqrt {10² - (4 - 3)² }\)   :  \(\sqrt { 10² - ( 4 + 3)² }\) 

        \(\sqrt {99 }\)          :         \(\sqrt { 51 }\) 

        \(\sqrt {33 }\)      :          \(\sqrt { 17 }\)