Dynamic Geometry: Incenter, Incircle, Excenter, Excircle, internal and external bisectors

Online Geometry

Note. Click the red button below to start the animation. Drag A, C, AC. Activate Step-by-Step bar and use the next step button

Incircle
The incircle or inscribed circle of a triangle ABC is the circle tangent to the three sides. The center I of the incircle is called the incenter. The incenter is the intersection of the three internal angle bisectors.

Excircle
An excircle or escribed circle of a triangle ABC is an external circle, tangent to one of its sides and tangent to the extensions of the other two. The center of an excircle, called an excenter, is the intersection of the internal bisector of one angle and the external bisectors of the other two. Every triangle has three excenters D, E, F, each tangent to one of the triangle's sides.

Tracenpoche

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.

Dynamic Software
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.

Instruction to explore the illustration above:

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

  • Manipulate. Drag points A and C to change the figure.

  • Step by Step construction. Press P and click the left mouse 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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