Yiu Triangle
YiuTriangle
The Yiu triangle DeltaO_AO_BO_C is the triangle formed by the centers of the Yiu circles.
It has area
| Delta^'=(f(a,b,c))/(a^4b^4c^4[1+2cos(2A)][1+2cos(2B)][1+2cos(2C)])Delta, |
where f(a,b,c) is a 12th-order polynomial and Delta is the area of the reference triangle DeltaABC.
The Yiu triangle is perspective with the following triangles.
triangle perspector Kimberling
tangential
triangle X_5-Ceva conjugate of X_3 X_(195)
See also
Yiu Circle, Yiu CirclesExplore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Yiu Triangle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/YiuTriangle.html