Simson Line:
Triangle, Point in the Circumcircle, Feet of
perpendiculars.
Level: High
School, SAT Prep, College

Hint to
interact with the figure below: Click the
red button ()
on the figure to start the animation. Drag points A, C, P, and line
AC to change the figure. Press P and click the left mouse button to start the step by step
construction, help.

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.

Dynamic Geometry: You can alter the figure
dynamically in order to test and prove (or disproved)
conjectures and gain mathematical insight that is less
readily available with static drawings by hand.

This page uses the
TracenPoche
dynamic geometry software and requires
Adobe Flash player 7 or higher.
TracenPoche is a project of Sesamath, an association of French
teachers of mathematics.

Instruction to explore the
dynamic figure:

Animation. Click the red
button
to start/stop animation

Manipulate. Drag points A,
C, and P and line AC to change the figure.

Step-by-Step construction.
Press P and click the left mouse
button
on any free area of the figure
above to show the
step-by-step bar and click 'Next
Step' button ()
to start the construction step-by-step:

Hide the step-by-step bar by
using again the combination P +
click left mouse.