Two circles having radii 12 cm and 8 cm, respectively, touch each other externally. A common tangent is drawn to these circles which touch the circles at M and N, respectively. What is the length (in cm) of MN?

$8\sqrt{6}$

Length of direct common tangent MN = \(\sqrt {d² - ( R - r )² }\)

= \(\sqrt {20² - ( 12 - 8 )² }\)

= \(\sqrt {400 - 16 }\)

= \(\sqrt {384 }\)

= 8\(\sqrt {6 }\) cm