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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.


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