Cevian Nest: What Is It About?
A Mathematical Droodle

Explanation

Copyright © 1996-2009 Alexander Bogomolny

The applet may suggest the following statement: Let A'B'C' be the cevian triangle of point P with respect to ABC. Let A''B''C'' be the cevian triangle of point P' with respect to A'B'C'. Then triangles ABC and A''B''C'' are perspective (from a point): the lines AA'', BB'', CC'' are concurrent.

(A'B'C' is called a cevian triangle triangle of point P with respect to ABC, if its vertices A', B', C' serve as the feet of the cevians AA', BB', CC' in ABC through point P.)

The configuration of three triangles inscribed into each other is known as Cevian Nest.

The problem has been proposed by H. Gülicher (#1581, Mathematics Magazine Vol. 72, No. 4, October 1999).

Menelaus and Ceva

• The Menelaus Theorem
• Menelaus Theorem: proofs ugly and elegant - A. Einstein's view
• Ceva's Theorem
• Ceva in Circumscribed Quadrilateral
• Ceva's Theorem: A Matter of Appreciation
• Ceva and Menelaus Meet on the Roads
• Menelaus From Ceva
• Menelaus and Ceva Theorems
• Ceva and Menelaus Theorems for Angle Bisectors
• Ceva's Theorem: Proof Without Words
• Cevian Nest
• Cevian Triangle
• An Application of Ceva's Theorem
• Trigonometric Form of Ceva's Theorem
• Two Proofs of Menelaus Theorem
• Simultaneous Generalization of the Theorems of Ceva and Menelaus
  • Theorems of Ceva and Menelaus, an Illustrated Generalization
  

  

  Copyright © 1996-2009 Alexander Bogomolny