- 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.
Deoclecio Gouveia Mota Junior
- The following paper has been published in Forum Geometricorum. It can be viewed at
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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