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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.

triangleperspectorKimberling
reference triangleX_5
tangential triangleX_5-Ceva conjugate of X_3X_(195)

See also

Yiu Circle, Yiu Circles

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Cite this as:

Weisstein, Eric W. "Yiu Triangle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/YiuTriangle.html

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