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RE: [EMHL] Locus

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  • Paul Yiu
    Dear Antreas, Let ABC be a triangle, P = (u:v:w) with cevian triangle A B C and Q=(x:y:z) with anticevian triangle QaQbQc. Denote A* = B Qc / C Qb, B* =
    Message 1 of 234 , Feb 1, 2013
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      Dear Antreas,

      Let ABC be a triangle, P = (u:v:w) with cevian triangle A'B'C' and Q=(x:y:z) with anticevian triangle QaQbQc.

      Denote A* = B'Qc /\ C'Qb, B* = C'Qa /\ A'Qc, C* = A'Qb /\ B'Qa.

      A*B*C* is perspective with

      (1) ABC at ( x/(-x/u+y/v+z/w) : y/(x/u-y/v+z/w) : z/(x/u+y/v-z/w)),
      (2) A'B'C' at Q,
      (3) QaQbQc at (x^2/u : y^2/v: z^2/w).

      Note: A'B'C' and QaQbQc are perspective at the cevian quotient
      P/Q = ( x(-x/u+y/v+z/w) : y(x/u-y/v+z/w) : z(x/u+y/v-z/w)).

      Best regards
      Sincerely
      Paul
    • Antreas Hatzipolakis
      ... [Telv Cohl] Pedal curve http://en.wikipedia.org/wiki/Pedal_curve -- http://anopolis72000.blogspot.com/
      Message 234 of 234 , Dec 4, 2014
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        [APH]:
        Let (O) be a fixed circle, Q a fixed point and P a point on the circle.

        Let Qp be the orthogonal projection of Q on the tangent to circle at P.

        Which is the locus of Qp as P moves on the circle?

        Generalization: (O) = a fixed conic.

        aph



        [Telv Cohl]

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