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Steiner Deltoid and Simson Lines
Steiner proved that the envelope of the Wallace-Simson lines is a curve that has three cuspidal points that is called the Steiner deltoid.
The Steiner Deltoid is tangent to the three sides of the triangle.
In this case, can you say where is the red point in the circumcircle in relation with some vertex of the triangle?
The Steiner Deltoid is tangent to the three altitudes of the triangle.
REFERENCES
Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer.
de Guzmán, Miguel 'The envelope of the Wallace-Simson lines of a triangle. A simple proof of the Steiner theorem on the deltoid'.
RACSAM, vol. 95, 2001.
Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: John Wiley and sons, 1969.
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Steiner deltoid is a hypocycloid related with the nine point circle of a triangle.
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