Intersections of lines and circles. (English) Zbl 1149.51011

Moses, Peter J. C.; Kimberling, Clark

Missouri J. Math. Sci. 19, No. 3, 176-187 (2007).

The authors of the paper under review present a method for determining barycentric coordinates of the point of intersection of a given line and a given circle. They apply their method to several lines (e.g. the Euler line, the circumcenter-incenter line, the Brocard axis) and several circles (e.g. the circumcircle, the incircle, the nine-point circle, the Brocard circle). They also apply the method to the point of intersection of two given lines, harmonic conjugate pairs, and to centers of similitude of pairs of circles.

Reviewer: Mowaffaq Hajja (Irbid)

MSC:

51N20	Euclidean analytic geometry
51M04	Elementary problems in Euclidean geometries

Keywords:

barycentric coordinates; Brocard axis; Brocard circle; center of similitude; circumcircle; harmonic conjugate pairs; incircle; nine-point circle