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.