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Cevian Nest: What Is It About?
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Copyright © 1996-2008 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.
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The problem has been proposed by H. Gülicher (#1581, Mathematics Magazine Vol. 72, No. 4, October 1999).
Copyright © 1996-2008 Alexander Bogomolny
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