GIF animation showing that tangency is preserved among circles if they expand or contract their radii in synch with one another.  Internally tangent circles must shrink and swell in tandem to preserve their tangency, whereas externally tangent circles must do the opposite: if one circle shrinks in radius by Δ<i>r</i>, the other must swell by the same amount.
<a href="//commons.wikimedia.org/wiki/User:WillowW" title="User:WillowW">WillowW</a>
CC BY 3.0
<span class="int-own-work" lang="en">Own work</span>