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Yiu Circle

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YiuCircle

The Yiu circle is the circumcircle of the Yiu triangle DeltaO_AO_BO_C.

It has center function given by

alpha=af(a,b,c),

where f(a,b,c) is a 14th-order polynomial. Its radius is

R_Y=(sqrt(g(a,b,c)))/(a^2b^2c^2|(4cos^2A-1)(4cos^2B-1)(4cos^2C-1)|)R,

where g(a,b,c) is a 12th-order polynomial and R is the circumradius of the reference triangle DeltaABC.

See also

Yiu Circles, Yiu Triangle

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Cite this as:

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

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