martes, 10 de enero de 2012

Orthology of Pedal and Cevian Triangles

In this article, I study the orthology of pedal and cevian triangles, and I identify the loci of the corresponding orthology centers.

Orthology of Pedal and Cevian Triangles

2 comentarios:

  1. How about the pedal and antipedal triangles of P (or P and Q, in general)?

    Anopolitis

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  2. Given a point Q = (u : v : w), for which points P = (x : y : z) are the pedal
    triangle of P and the pedal triangle of Q orthologic?

    We have the following results:

    1. The locus of points P = (x : y : z) such that the pedal triangle A1B1C1 of P
    and the pedal triangle A2B2C2 of Q are orthologic is the line OQ.
    2. The locus of the orthology center of A1B1C1 with respect to A2B2C2 is a line
    through the orthocenter of A2B2C2.
    3. The locus of the orthology center of A2B2C2 with respect to A1B1C1 is the
    rectangular hyperbola through P with respect to the triangle A2B2C2.

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