Simson Line
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High Quality Content by WIKIPEDIA articles! In geometry, given a triangle and a point on its circumcircle, the intersections formed when lines are constructed from the point perpendicular to each of the triangle's sides are collinear. The line through these points is the Simson line, named for Robert Simson. The concept was first published, however, by William Wallace.The converse is also true; if the feet of the perpendiculars dropped from a point to the sides of the triangle are collinear, then the point is on the circumcircle. The Simson line of a point is just the pedal triangle of it; the...
High Quality Content by WIKIPEDIA articles! In geometry, given a triangle and a point on its circumcircle, the intersections formed when lines are constructed from the point perpendicular to each of the triangle's sides are collinear. The line through these points is the Simson line, named for Robert Simson. The concept was first published, however, by William Wallace.The converse is also true; if the feet of the perpendiculars dropped from a point to the sides of the triangle are collinear, then the point is on the circumcircle. The Simson line of a point is just the pedal triangle of it; the case when that pedal triangle degenerates to a line.
