Gergonne in Ellipse

The lines joining the points of tangency of the incircle with the opposing vertices of a triangle concur in a point known as the Gergonne point or Gergonne's center.

Since, under projective mappings, the straight lines are mapped onto the straight lines and the tangency and concurrency are preserved, the existence of the Gergonne point is assured under projective mappings. However, the image of a circle may become any non-degenerate conic section. The applet below illustrates this fact for an ellipse inscribed in a triangle.

Conic Sections > Ellipse

• What Is Ellipse?
  
• Analog device simulation for drawing ellipses
• Angle Bisectors in Ellipse
• Angle Bisectors in Ellipse II
• Between Major and Minor Circles
• Brianchon in Ellipse
• Butterflies in Ellipse
• Conjugate Diameters in Ellipse
• Dynamic construction of ellipse and other curves
• Ellipse in Arbelos
• Ellipse Between Two Circles
• Euclidean Construction of Center of Ellipse
• Euclidean Construction of Tangent to Ellipse
• Focal Definition of Ellipse
• Focus and Directrix of Ellipse
• From Foci to a Tangent in Ellipse
• Gergonne in Ellipse
• Pascal in Ellipse
• La Hire's Theorem in Ellipse
• Optical Property of Ellipse
• Parallel Chords in Ellipse
• Poncelet Porism in Ellipses
• Reflections in Ellipse
• Three Squares and Two Ellipses
• Three Tangents, Three Chords in Ellipse

Copyright © 1996-2009Alexander Bogomolny