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.


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.



Home | Geometry | Collinear Points | Dynamic Geometry | TracenPoche | Simson Line | Triangles | Circumcircle | Perpendicular lines | Email | By Antonio Gutierrez