Question

Circles O and P are tangent and have radii of 16 and 4, respectively. Find the length of their common tangent.

Answer 1

\[(r - s)^{2} + x ^{2} = (r + s)^{2}\]
\[x ^{2} = (r + s)^{2} - (r - s)^{2}\]
\[x ^{2} = r ^{2} + 2rs + s ^{2} - r ^{2} + 2rs - s ^{2}\]
\[x ^{2} = 4rs\]
\[x = 2\sqrt{rs}\]