Go Geometry Education

Triangle, Three Medians, Six Concyclic Circumcenters with Dynamic Geometry: TracenPoche Software. Level: High School, College, Mathematics Education.

Proposition: Medians AD, BE, and CF split a triangle ABC into six smaller triangles. Prove that their circumcenters O1, O2, O3, O4, O5, and O6 are concyclic (lie on a circle called van Lamoen circle).

Interact with the figure below: Click the red button () on the figure to start the animation. Drag A, C, or AC to change the figure. Press P and click the left mouse button to start the step by step construction, use the next step button
 


 

Interactive Geometry Software or Dynamic Geometry: You can alter the figure above 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 theorem above:

  • Animation. Click the red button to start/stop animation

  • Manipulate. Drag red points to change the figure.

  • Step by Step construction. Press P and click the left mouse button on any free area to show the step-by-step bar and start the construction:
     
    Hide the step-by-step bar by using again the combination P + click left mouse.

 

Home | Geometry | Dynamic Geometry | TracenPoche Index | Using Geometry Designer | Problem 847 | Triangles | van Lamoen Circle | Concurrent lines | Email Post a comment | By Antonio Gutierrez