info prev up next book cdrom email home

Purser's Theorem

\begin{figure}\begin{center}\BoxedEPSF{PursersTheorem.epsf}\end{center}\end{figure}

Let $t$, $u$, and $v$ be the lengths of the tangents to a Circle $C$ from the vertices of a Triangle with sides of lengths $a$, $b$, and $c$. Then the condition that $C$ is tangent to the Circumcircle of the Triangle is that

\begin{displaymath}
\pm at\pm bu\pm cv=0.
\end{displaymath}

The theorem was discovered by Casey prior to Purser's independent discovery.

See also Casey's Theorem, Circumcircle




© 1996-9 Eric W. Weisstein
1999-05-26