Purser's Theorem
PursersTheorem
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
| +/-at+/-bu+/-cv=0. |
The theorem was discovered by Casey prior to Purser's independent discovery.
See also
Casey's Theorem, CircumcircleExplore with Wolfram|Alpha
WolframAlpha
More things to try:
Cite this as:
Weisstein, Eric W. "Purser's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PursersTheorem.html