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• Dear Alexey Thank you for your interesting remark about the radii of these 4 circles. As for me, I only use this elementary theorem: The locus of the points M
Message 1 of 476 , Dec 5 5:13 AM
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Dear Alexey
As for me, I only use this elementary theorem:
The locus of the points M such that the bissectors of angle (MA, MB) are
parallel to 2 orthogonal directions (L) and (L') is a rectangular hyperbola
of center the middle O of AB, through A and B and with asymptots parallel to
(L) and (L').

Besides it is strange that M. Bataille don't give explicitely the loci of
the vertices A, B, C, D, even if they are obtained by mere translations
from the loci of the middles of the segments AC and BD.

Friendly
Francois

PS
Where this Town Tournament takes place?

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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
Message 476 of 476 , Apr 16
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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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