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Gallatly Circle


GallatlyCircle

The Gallatly circle is the circle with center at the Brocard midpoint X_(39) and radius

R_G=Rsinomega
(1)
=(abc)/(2sqrt(a^2b^2+a^2c^2+b^2c^2)),
(2)

where R is the circumradius of the reference triangle and omega is the Brocard angle.

It has circle function

 l=(bc(a^2+b^2+c^2)(a^4-a^2b^2-a^2c^2-2b^2c^2))/(4(a^2b^2+a^2c^2+b^2c^2)^2),
(3)

corresponding to Kimberling center X_(183).

It is a Tucker circle with parameter

 lambda=sin^2omega
(4)

and parametric angle

 phi=1/2pi-omega,
(5)

where omega is the Brocard angle.

The Gallatly circle passes through Kimberling centers X_(2026) and X_(2027) (the intersections with the Brocard axis).


See also

Central Circle, Tucker Circles

Explore with Wolfram|Alpha

Cite this as:

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

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