The Steiner deltoid is the envelope of the Simson
lines of a triangle.
Its circumcircle is the Steiner circle , and its incircle is the nine-point
circle .
The triangle formed by vertices of the deltoid is homothetic to the first Morley triangle , with the center dividing the line
The triangle formed by the deltoid's meets with the nine-point circle is also is homothetic to the first
Morley triangle , with the center dividing the line
See also Deltoid ,
First Morley Triangle ,
Simson Line ,
Steiner
Circle
This entry contributed by Peter Moses
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References Butchart, J. H. "The Deltoid Regarded as the Envelope of Simson Lines." Amer. Math. Monthly 46 , 85-86, 1939. de
Guzmán, M. "The Envelope of the Wallace-Simson Lines of a Triangle: A
Simple Proof of the Steiner Theorem on the Deltoid." Dec. 1998. http://www.mat.ucm.es/deptos/am/guzman/deltoide121298/00delten.htm . Dörrie,
H. "Steiner's Three-Pointed Hypocycloid." §53 in 100
Great Problems of Elementary Mathematics: Their History and Solutions. Lockwood, E. H. A
Book of Curves. Wells,
D. The
Penguin Dictionary of Curious and Interesting Geometry. Zwikker, C. The
Advanced Geometry of Plane Curves and Their Applications. Referenced on Wolfram|Alpha Steiner Deltoid
Cite this as:
Moses, Peter . "Steiner Deltoid." From MathWorld Eric
W. Weisstein . https://mathworld.wolfram.com/SteinerDeltoid.html
Subject classifications
in the ratio of their side lengths,
in the ratio of their side lengths
