data-ad-format="horizontal">



 
Incenter of a Triangle
Geometry construction using a compass and straightedge

This page shows how to construct (draw) the incenter of a triangle with compass and straightedge or ruler. The Incenter of a triangle is the point where all three angle bisectors always intersect, and is the center of the triangle's incircle. See Constructing the incircle of a triangle.

In this construction, we only use two bisectors, as this is sufficient to define the point where they intersect, and we bisect the angles using the method described in Bisecting an Angle. The point where the bisectors cross is the incenter.

Printable step-by-step instructions

The above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.

Proof

The image below is the final drawing from the above animation.

  Argument Reason
1 RC is the bisector of the angle PRQ. By construction. See Bisecting an angle with compass and straightedge for method and proof.
2 QC is the bisector of the angle PQR. By construction. See Bisecting an angle with compass and straightedge for method and proof.
3 C is the incenter of the triangle The incenter of a triangle is the point where the angle bisectors intersect. See Incenter of a triangle.

  - Q.E.D

Try it yourself

Click here for a printable incenter worksheet containing two problems to try. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.

Other constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions