Question

Write the formula for length of common tangent of two circles touching externally.

Answer 1

Considering two circles of different radius as r1 and r2 eith their centres are denoted as O and O’ respectively. These two circles are in position just by touching in a single point as shown the figure.

Let PQ be the common tangent of the two circles.  

When we imaginarily draw a segment OR parallel to PQ, the formula we get the way of finding the length of PQ as both will be one and the same. Then it is given by,

Length of PQ = $\sqrt{4r_1r_2}$