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.
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Copyright © 1996-2018Alexander Bogomolny