The Simson Line Theorem states that the feet of the perpendiculars dropped from a point on a triangle's circumcircle to each of its three sides, extended if necessary, are always collinear, a property that fails for a point not on the circumcircle. Traditionally named for Robert Simson, though the result is now generally credited to William Wallace, it is a classical result of triangle geometry, and the resulting line is called the Simson line.
Facts
StatementGiven a triangle ABC and a point P on its circumcircle, the feet of the perpendiculars from P to the three sides of the triangle are collinear. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Simson line - Wikipedia
Sources
1. Simson line - Wikipedia
Lead section
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.
In Branch: Geometry, Lead sentence
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 col
View the Source2. Wikidata: Simson Line Theorem
LeadQuote, Lead
The concept was first published, however, by William Wallace in 1799
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.