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Forum Geometricorum

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  • ForumGeom
    The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2010volume10/FG201004index.html The editors Forum
    Message 1 of 476 , Mar 1, 2010
      The following paper has been published in Forum Geometricorum. It can be
      viewed at

      http://forumgeom.fau.edu/FG2010volume10/FG201004index.html

      The editors
      Forum Geometricorum
      ===========================================
      Nicolae Anghel, A maximal parallelogram characterization of ovals having
      circles as orthoptic curves,
      Forum Geometricorum, 10 (2010) 21--25.

      Abstract: It is shown that ovals admitting circles as orthoptic curves
      are precisely characterized by the property that every one of
      their points is the vertex of exactly one maximal-perimeter inscribed
      parallelogram. This generalizes an old property of ellipses, most recently
      revived by Connes and Zagier in the paper A Property of Parallelograms
      Inscribed in Ellipses.

      [Non-text portions of this message have been removed]
    • 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
        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.


        [Non-text portions of this message have been removed]
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