The Yiu -circle
of a reference triangle is the circle passing through vertex and the reflections of vertices and
with respect to the opposite sides. The Yiu - and -circles
are then analogously defined.

The -circle has center

(1)

which can also be written

(2)

(P. Moses, pers. comm., Jan. 31, 2005).

Its -radius is

where ,
, , and are Conway triangle
notation ,
is the circumcenter , and is the orthocenter (P. Moses,
pers. comm., Jan. 31, 2005).

The Yiu circles powers with respect to the vertices are

The Yiu circles mutually intersect in a single point, which is therefore their radical center . It has center function

(10)

which is Kimberling center (the inverse in the circumcircle of the Kosnita
point ).

The Yiu circles do not have a radical circle .

See also Reflection ,

Yiu
Circle ,

Yiu Triangle
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Cite this as:
Weisstein, Eric W. "Yiu Circles." From
MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/YiuCircles.html

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