This is the third part of the Geometer’s Sketchpad Essentials Series. In this tutorial, we are going to construct the incircle of a triangle. In doing so, we are going to learn how to use the *Compass tool* and construct *Angle bisectors*.

**Step by Step Instructions**

1.) Using the **Segment tool**, construct a triangle.

2.) Select the **Text tool** and click each vertex to reveal their names. GSP will name the triangle *ABC*.

3.) To construct the angle bisector of angle *A*, deselect all the objects, and then click the vertices in the following order: *B*, *A*, *C* (or *C*, *A*, *B*).

4.) Next, click the **Construct** menu from the menu bar and choose **Angle Bisector**. This will produce a ray bisecting angle *A*. Now, construct the the angle bisector for angle *B*.

5.) To intersect the two rays, deselect all the objects, click the two rays, and choose **Intersection** from the **Construct** menu. The intersection of the two rays will be the center of our circle.

6.) Now, hide the bisector by clicking the **Hide Bisectors** from the **Display** menu, and use the **Text tool** to display the name of the intersection point. This is named *D*.

7.) The *incircle* is tangent to the sides of the triangle. To create the point of tangency, we create a point on one of the sides that is perpendicular to *D *(Why?). To do this, select segment *AB* (be sure **not** to include points *A* and *B*), select point *D*, click the **Construct** menu, and then click **Perpendicular Line**.

8.) Select the *perpendicular line* and segment *AB*, and choose **Intersection** from the **Construct** menu to construct the intersection. Use the **Text** **tool** and name the intersection *E*.

9.) To construct the incircle, click the **Compass tool**, click point *D*, and then click point *E*.

10.) Now, hide the perpendicular line passing through *D* by selecting it, and then clicking **Hide Perpendicular** **Line** from the **Display** menu.

11.) Now, move the vertices of the triangle. What do you observe?

The circle with center us inscribed to triangle *ABC*. This circle is called the *incircle* of triangle *ABC*.