matematicas visuales visual math

Steiner proved that the envelope of the Wallace-Simson lines is a curve that has three cuspidal points that is called the Steiner deltoid.

Steiner Deltoid: envelope of the Wallace-Simson lines | matematicasVisuales
Steiner Deltoid: envelope of the Wallace-Simson lines | matematicasVisuales

The Steiner Deltoid is tangent to the three sides of the triangle.

Steiner Deltoid: The Steiner Deltoid is tangent to the three sides of the triangle | matematicasVisuales

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.

Steiner Deltoid: The Steiner Deltoid is tangent to the three altitudes of the triangle | matematicasVisuales

REFERENCES

Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer.
Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: John Wiley and sons, 1969.

MORE LINKS

Wallace-Simson lines
Each point in the circle circunscribed to a triangle give us a line (Wallace-Simson line)
The deltoid and the Morley triangle
Steiner Deltoid and the Morley triangle are related.
Central and inscribed angles in a circle
Central angle in a circle is twice the angle inscribed in the circle.
Central and inscribed angles in a circle | Mostration | Case I
Interactive 'Mostation' of the property of central and inscribed angles in a circle. Case I: When the arc is half a circle the inscribed angle is a right angle.
Central and inscribed angles in a circle | Mostration | Case II
Interactive 'Mostation' of the property of central and inscribed angles in a circle. Case II: When one chord that forms the inscribed angle is a diameter.
Central and inscribed angles in a circle | Mostration | General Case
Interactive 'Mostation' of the property of central and inscribed angles in a circle. The general case is proved.
Drawing fifteen degrees angles
Using a ruler and a compass we can draw fifteen degrees angles. These are basic examples of the central and inscribed in a circle angles property.
Morley triangle
If we trisect the angles of a triangle and consider the three intersection points of corresponding trisector lines we always get an equilateral triangle (Morley's triangle)