\input CS445Hdr
\def\file{CS445NJunk.tex of November 9, 1982 4:26 PM}
\def\header{Miscellaneous Junk}
\def\title{Junk}
This result is particularly useful when combined with the next lemma:

\lemma{8.4{\rm {(the Bubble lemma)}}{Let C1, C2 be two circles passing through the points $p$ and $q$, and let $c1̌, c2̌$ be their centers. Then a point $r$ is inside $C1̌$ but not $C2̌$ iff the circumcenter of $p, q$ and $r$ lies on the open segment $c1̌c2̌$.}
\proof{{\bf ???}}

For example, we have the following corollary:

\lemma{8.5}{If two points $u, v$ belong to exactly the same $m$ Voronoi regions