Simson line
Line defined from a triangle and a point on its circumcircle, through the closest point on each side line to the given point
Nº Q937921 ★★★
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Simson line
Line defined from a triangle and a point on its circumcircle, through the closest point on each side line to the given point
In geometry, given a triangle ABC and a point P on its circumcircle, the three closest points to P on lines AB, AC, and BC are collinear. The line through these points is the Simson line of P, named for Robert Simson.
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In geometry, given a triangle ABC and a point P on its circumcircle, the three closest points to P on lines AB, AC, and BC are collinear. The line through these points is the Simson line of P, named for Robert Simson. The concept was first published, however, by William Wallace in 1799, and is sometimes called the Wallace line. The converse is also true; if the three closest points to P on three lines are collinear, and no two of the lines are parallel, then P lies on the circumcircle of the triangle formed by the three lines. Or in other words, the Simson line of a triangle ABC and a point P is just the pedal triangle of ABC and P that has degenerated into a straight line and this condition constrains the locus of P to trace the circumcircle of triangle ABC.
Texto: Wikipédia em inglês, CC BY-SA 4.0. · Imagem: Inductiveload (Public domain) ·
