## GeoGebra Essentials 3 – Triangles, Incircles, and Circumcircles

This is the third tutorial in the **GeoGebra Essentials Series**. If you are entirely new to GeoGebra, you should read the** Introduction to GeoGebra **post and prior tutorials. It contains the pre-requisites of this tutorial.

In the tutorial below, menu commands, located in the menu bar, are **in brown bold text**, and submenus are denoted by the **>** symbol. For example, **Options>Labeling> New Points Only** means, click the **Options** menu, choose **Labeling** from the list, then select **New Points Only**. The GeoGebra tools are denoted by **orange bold texts**. For example, **New Point** means the new point tool.

In this tutorial, we show that in any triangle, we can always create a circle passing through its three vertices, and we can always create an inscribed circle. The circle that passes through the three vertices of a triangle is called the *circumcircle* of the triangle, while the inscribed circle is called its *incircle*.

To create the circumcircle of triangle ** ABC**, we find the intersection of the

*perpendicular bisectors*of its three sides. The intersection, known as the circumcenter, will be the center of the

*circumcircle*. To construct the incircle, we find the intersection of the three

*angle bisectors*of its interior angles. The intersection, known as the incenter, will be the center of the incircle. » Read more