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- Simson_line abstract "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 1797.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.".
- Simson_line thumbnail Pedal_Line.svg?width=300.
- Simson_line wikiPageExternalLink JavaGSPLinks.htm.
- Simson_line wikiPageExternalLink miquel.html.
- Simson_line wikiPageExternalLink Simpson.shtml.
- Simson_line wikiPageID "3307757".
- Simson_line wikiPageRevisionID "581492046".
- Simson_line hasPhotoCollection Simson_line.
- Simson_line title "Simson Line".
- Simson_line urlname "SimsonLine".
- Simson_line subject Category:Triangle_geometry.
- Simson_line comment "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 1797.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.".
- Simson_line label "Droite de Simson".
- Simson_line label "Rechte van Wallace".
- Simson_line label "Recta de Simson".
- Simson_line label "Retta di Simson".
- Simson_line label "Simson line".
- Simson_line label "Simsonsche Gerade".
- Simson_line label "Прямая Симсона".
- Simson_line label "シムソンの定理".
- Simson_line label "西姆松定理".
- Simson_line sameAs Simsonsche_Gerade.
- Simson_line sameAs Recta_de_Simson.
- Simson_line sameAs Droite_de_Simson.
- Simson_line sameAs Retta_di_Simson.
- Simson_line sameAs シムソンの定理.
- Simson_line sameAs Rechte_van_Wallace.
- Simson_line sameAs m.094q33.
- Simson_line sameAs Q937921.
- Simson_line sameAs Q937921.
- Simson_line wasDerivedFrom Simson_line?oldid=581492046.
- Simson_line depiction Pedal_Line.svg.
- Simson_line isPrimaryTopicOf Simson_line.
