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Re: [EMHL] Re: Median line

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  • Etienne Rousee
    ... Yes, and is the line maximizing the sum the other axis of the Steiner ellipse ? I was mistaken because I experimented whis the sum of the distances and
    Message 1 of 476 , Mar 10 4:32 AM
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      Le 08/03/2011 19:09, jpehrmfr a écrit :
      >> Is the line L, minimizing the sum of
      >> the squares of the distance from A,B,C
      >> to L, always a median of ABC ?
      >
      > No, this line is the focal axis of the Steiner ellipses

      Yes, and is the line maximizing the sum the other
      axis of the Steiner ellipse ?
      I was mistaken because I experimented whis the sum
      of the distances and forgot the squares.
      In this case, it seems near a median.

      --

      Etienne
    • forumgeom forumgeom
      The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2013volume13/FG201309ndex.html The editors Forum
      Message 476 of 476 , Apr 16, 2013
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        The following paper has been published in Forum Geometricorum. It can be viewed at

        http://forumgeom.fau.edu/FG2013volume13/FG201309ndex.html

        The editors
        Forum Geometricorum

        Paul Yiu, On the conic through the intercepts of the three lines through the centroid and the intercepts of a given line,
        Forum Geometricorum, 13 (2013) 87--102.

        Abstract. Let L be a line intersecting the sidelines of triangle ABC at X, Y, Z respectively. The lines joining these intercepts to the centroid give rise to six more intercepts on the sidelines which lie on a conic Q(L,G). We show that this conic (i) degenerates in a pair of lines if L is tangent to the Steiner inellipse, (ii) is a parabola if L is tangent to the ellipse containing the trisection points of the sides, (iii) is a rectangular hyperbola if L is tangent to a circle C_G with center G. We give a ruler and compass construction of the circle C_G. Finally, we also construct the two lines each with the property that the conic Q(L,G) is a circle.


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