Step-by-step Instructions

After doing this	Your work should look like this
We start with the given triangle.
1.  Place the compass point on any of the triangle's vertices. Adjust the compass to a medium width setting. The exact width is not important.
2.  Without changing the compass width, strike an arc across each adjacent side.
3.  Change the compass width if desired, then from the point where each arc crosses the side, draw two arcs inside the triangle so that they cross each other, using the same compass width for each.
4.  Using the straightedge, draw a line from the vertex of the triangle to where the last two arcs cross.
5.  Repeat all of the above at any other vertex of the triangle. You will now have two new lines drawn.
6.  Done. Mark a point where the two new lines intersect. This is the incenter of the triangle.
7.  (Optional) Repeat steps 1-4 for the third vertex. This will convince you that the three angle bisectors do, in fact, always intersect at a single point. But two are enough to find that point.

Explanation of method

As can be seen in Incenter of a Triangle, the three angle bisectors of any triangle always pass through its incenter. In this construction, we only use two, as this is sufficient to define the point where they intersect. We bisect the two angles using the method described in Bisecting an Angle. The point where the bisectors cross is the incenter.

The incenter you just constructed is the center of the triangle's incircle. See Constructing the incircle of a triangle.

Constructions pages on this site

Lines

• Introduction to constructions
• List of printable constructions worksheets
• Copy a line segment
• Parallel line through a point
• Perpendicular bisector of a line segment
• Perpendicular from a line at a point
• Perpendicular from a line through a point
• Perpendicular from endpoint of a ray
• Divide a segment into n equal parts

Angles

• Bisecting an angle
• Copy an angle
• Construct a 30° angle
• Construct a 45° angle
• Construct a 60° angle
• Construct a 90° angle (right angle)
• Constructing  75°  105°  120°  135°  150° angles and more

Triangles

• Copy a triangle
• Isosceles triangle, given base and side
• Isosceles triangle, given base and altitude
• Equilateral triangle
• Triangle medians
• 30-60-90 triangle, given the hypotenuse
• Triangle, given 3 sides (sss)
• Triangle, given one side and adjacent angles (asa)
• Triangle, given two sides and included angle (sas)
• Incircle of a triangle
• Circumcircle of a triangle

Triangle Centers

• Triangle incenter
• Triangle circumcenter
• Triangle orthocenter
• Triangle centroid

Circles, Arcs and Ellipses

• Finding the center of a circle
• Circle given 3 points
• Tangent at a point on the circle
• Tangents through an external point
• Focus points of a given ellipse

Non-Euclidean constructions

• Construct an ellipse with string and pins
• Find the center of a circle with any right-angled object