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New construction of the Tarry point

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  • Steve Sigur
    Hello all in geometry, I have always found the Tarry point mysterious. It is opposite the Steiner point in the circumcircle and the intersection of the
    Message 1 of 1 , Apr 2 7:48 PM
      Hello all in geometry,

      I have always found the Tarry point mysterious. It is opposite the
      Steiner point in the circumcircle and the intersection of the
      circumcircle with the Kiepert hyperbola. Both of these are nice, if
      disconnected properties.

      I have a new construction which both explains the above and shows
      that the Tarry point is one example of a universal phenomenon.

      We begin as I always begin, with a single point in the plane of the
      triangle. We will choose this point to be K, the symmedian point.

      There are now two natural lines, the dual of K and G—K. Natural in
      this context means that the structure is affine invariant. The
      endpoints of these lines map to antipodal points on the Steiner ellipse.

      These lines meet at P. The isotomic of the two lines are
      circumconics, one, the Kiepert hyperbola, has its perspector tS at
      infinity, the second has perspector K. The isotomic of P is the
      intersection between these conics. This is the Tarry point.

      The constuction shows that this is construction is general. Slightly
      more analysis shows that S and T are opposite on the K circumconic
      and that this too is general.

      Friendly,

      Steve




      Triangle web page:
      http://paideiaschool.org/TeacherPages/Steve_Sigur/geometryIndex.htm

      Other math:
      http://paideiaschool.org/TeacherPages/Steve_Sigur/interesting2.htm
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