Intersections of Lines and Circles

Abstract

A method is presented for determining barycentric coordinates of points of intersection of a line and a circle. The method is applied specifically to the Euler line, the line of the circumcenter and incenter, the Brocard axis, and several circles, including the circumcircle, incircle, nine-point circle, and Brocard circle. The method also applies to intersections of certain pairs of lines, harmonic conjugate pairs, and to centers of similitude of pairs of circles.