## Forum Geometricorum

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• Dear Friends, I submitted the my paper Sawayama-Thebault s Theorem to Forum Geometricorum, see hyacinthos message #20244. In response, the anonymous referee
Message 1 of 476 , Sep 28, 2011
Dear Friends,

I submitted the my paper Sawayama-Thebault's Theorem to Forum Geometricorum, see hyacinthos message #20244.
In response, the anonymous referee said that the article is unreadable in present format.
I always learned that there are only two types of geometric solutions: The right or wrong.
The referee has invented another type of geometric solution: unreadable.
So, I would like you to read my solution to the problem and tell me if it is correct or wrong or unreadable.

Sincerely,

Deoclecio Gouveia Mota Junior
• 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.

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