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.

See complete interactive figure

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

Post your solutions or ideas in the comments.

## Wednesday, July 9, 2008

### Interactive Simson Line

Labels:
angle,
circumcircle,
collinear,
cyclic quadrilateral,
foot,
line,
orthic triangle,
perpendicular,
Simson

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