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Purser's Theorem


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

\pm at\pm bu\pm cv=0.

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

See also Casey's Theorem, Circumcircle

© 1996-9 Eric W. Weisstein