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Circle X(4)X(15)X(16)

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  • michgarl
    Dear colleagues This circle has for barycentric equation a²vw+b²wu+c²uv +k(u+v+w)(mu+nv+pw) = 0 with k = S²(b²-c²)(c²-a²)(a²-b²)/a²b²c m =
    Message 1 of 1 , Feb 20, 2008
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      Dear colleagues
      This circle has for barycentric equation
      a²vw+b²wu+c²uv +k(u+v+w)(mu+nv+pw) = 0
      with k = S²(b²-c²)(c²-a²)(a²-b²)/a²b²c
      m = S_a(b²-c²)(S²+S_bc)/a²
      n = S_b(c²-a²)(S²+S_ac)/b²
      p = S_c(a²-b²)(S²+S_ab)/c²
      with S² =S_bc+S_ac+S_ab ; S_a = (C-A)(B-A); S_bc =S_b*S_c
      (Notations from Conway)
      The center of that circle is
      [a²S_a(b²-c²)(S²+S_bc):b²S_b(c²-a²)(S²+S_ac): c²S_c(a²-b²)(S²+S_ab)]
      Is it in ETC?
      Is that circle in Mathworld?
      Good Luck

      Michel
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