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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, Circumcircle

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Cite this as:

Weisstein, Eric W. "Purser's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PursersTheorem.html

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