# How to Inscribe a Circle in a Triangle

 Click on the blue points and drag them to change the figure. Can the incenter (point D) be outside the triangle? How do you know. Manipulative 1 - Inscribed Triangle Created with GeoGebra.
StepExampleDescription
2 Draw the angle bisector of angle ABC.
3 Draw the angle bisector of angle BCA. For steps 2 and 3, any two angles can be bisected.
4 Draw point D at the intersection of the angle bisectors.
5 Draw a line through point D perpendicular to side AB. Note that this line can be perpendicular to any of the sides.
6 Mark point E at the intersection of the perpendicular and side AB.
7 Draw a circle with center at D with a radius of DE.

#### Understanding Check

Use the GeoGebra application below to construct the circumscribing circle about the rectangle.

 Click on the blue points and drag them to change the figure. Manipulative 2 - How to inscribe a circle in a triangle using Geogebra Created with GeoGebra.
1. Click on the down arrow of the construction to open the construction menu. Select the Angle Bisector menu item. Then click on points B, A, then C. You have constructed the angle bisector of angle BAC.
2. Now click on point A, B, then C. You have constructed the angle bisector of angle ABC.
3. Click on the down arrow of the Point menu button . Select the Intersect Two Objects menu button. Click on each of the two angle bisectors. Point D that appears at the intersection of the two angle bisectors is the incenter.
4. Click on the arrow in the angle bisector menu button to open the construction menu. Click on the perpendicular line menu button . Now click on the incenter (point C) then one side of the triangle. The point where the perpendicular line intersects the side of the triangle is on the incircle.
5. Click on the Intersect Two Objects button, then click on the perpendicular line, and the side to which it is perpendicular. Point E appears. Point E is on the incircle.
6. Click on the Circle With Center Through Point . Then click on the incenter (point D) then point E. The circle that is drawn is the incircle.

To change the manipulative, first click on the arrow menu button. Then click on the blue points and drag them to change the figure.

Table 2: Inscribing a circle in a triangle.

McAdams, David E. How to Inscribe a Circle in a Triangle. 4/22/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/h/htinscribetriangle.html.

### Revision History

4/22/2019: Update equations and expressions to new format. (McAdams, David E.)