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Steiner Angles


The angles S_1=A_1/2 and S_2=A_2/2 obtained from solving

 sin(x+omega)=2sinomega
(1)

for x=A_1,A_2, where omega is the Brocard angle. The half-angles A_1 and A_2 are given by

cot(1/2A_1)=cotomega-sqrt(cot^2omega-3)
(2)
cot(1/2A_2)=cotomega+sqrt(cot^2omega-3)
(3)

(Gallatly 1913, p. 98).


See also

Brocard Angle

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References

Gallatly, W. "The Steiner Angles." §137 in The Modern Geometry of the Triangle, 2nd ed. London: Hodgson, p. 98, 1913.

Referenced on Wolfram|Alpha

Steiner Angles

Cite this as:

Weisstein, Eric W. "Steiner Angles." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SteinerAngles.html

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