The Simson Line: Theorems and Problems Index

Index
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The Simson Line Index
Level: High School, SAT Prep, College geometry

Angle between two Simson Lines.

In the illustration, the angle between the Simson lines SIM and S'I'M' of the points P and P' is half the measure of the arc PP'.


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Simson Line

The Simson line is the Line SIM containing the feet S, I, and M of the perpendiculars from a point P on the circumcircle of a triangle ABC to the sides (or their extensions) of the triangle.


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gogeometry.com/simsontheorem1.html

Interactive Simson Line

Proposition
Given a triangle ABC and P a point on its circumcircle, as shown. Prove that the feet D, E, and F of the perpendiculars drawn from P to the sides (or their extensions) are collinear. The line DEF is called the Simson line.



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Triangle, Circumcircle, Perpendiculars, Collinear feet points. Level: High School, SAT Prep, College geometry

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