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Re: [EMHL] A simple triangle construction?..

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  • Philippe
    ... Dear Luis, Yes it is. Your U_c = my W = pole of symmedian with respect to circumcircle = harmonic conjugate of T_c /AB This results into a construction
    Message 1 of 10 , Jun 8, 2010
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      Luís Lopes wrote:
      >
      > 1) [ to construct triangle ABC, given AB, angle A and foot T_c of
      > symmedian ]
      >
      > Let t_c be the tangent to the circumcircle of ABC at C and U_c
      > be the intersection (A,B)/\t_c.
      >
      > Trying to solve this problem I browsed a book of mine and read that
      > H (U_c,A,T_c,B) are Harmonic conjugates. Then one can construct U_c.
      >
      > Would there be a construction based on this?
      > I wonder whether U_c==W in <http://cjoint.com/?gioshSeBLy>
      >

      Dear Luis,

      Yes it is.
      Your U_c = my W = pole of symmedian with respect to circumcircle
      = harmonic conjugate of T_c /AB

      This results into a construction like :
      Construct W = U_c = harmonic conjugate of T_c wrt AB
      Then WC = tangent in C from W to circumcircle of ABC.
      Thus a locus for C : circle with radius WC with WC^2 = WA.WB

      The given construction is to draw W and this locus at once from a specific
      easy constructed point "A" on this locus : point D.
      (avoiding the separate effective constructions of harmonic conjugates,
      and of radius from R^2 = WA.WB)

      Regards.
      Philippe
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