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## Hello from Sevilla

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• Dear friends Hyacinthos: in http://personal.us.es/rbarroso/trianguloscabri/   you can see 628 and 629 issues of the journal Research TRIANGULOSCABRI that the
Message 1 of 476 , Nov 1, 2011
Dear friends Hyacinthos:
in

http://personal.us.es/rbarroso/trianguloscabri/

you can see 628 and 629 issues of the journal Research

TRIANGULOSCABRI

that the course has in yeartwelve.

This time it's a line that Professor

Izquierdo Asensi
Formulas and Geometric Properties

http://www.casadellibro.com/libro-formulas-y-propiedades-geometricas/9788493366841/1098595

and generalization I have raised.

Best regards from Sevilla

Ricardo Barroso

http://personal.us.es/rbarroso/

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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, 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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