Feuerbach Points and Nine-Point Circle with Dynamic Geometry: TracenPoche Software.
Incircle, Excircles, Tangent Circles,
Tangency Points. Level: High School, College,
Mathematics Education.

Proposition: The
nine-point circle of any triangle
is tangent internally to the
incircle at a point
F called the
Feuerbach point, and tangent
externally to the three
excircles at F1, F2, and F3.

Interact with the figure below: Click the
red button ()
on the figure to start the animation. Drag points A, C, and line
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 points A
and C, and line AC 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.