How to construct (draw) circumcenter of a triangle with compass and straightedge or ruler

Circumcenter of a Triangle

Geometry construction using a compass and straightedge

- Printable problem worksheet
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Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping. (If there is no image below, see support page.)

Step-by-step Instructions

This construction assumes you are already familiar with Constructing the Perpendicular Bisector of a Line Segment.

After doing this	Your work should look like this
We start with a triangle ABC.
1. Find the bisector of one of the triangle sides. Any one will do. See Constructing the Perpendicular Bisector of a Line Segment for detailed instructions.
2. Repeat for the another side. Any one will do.
3. Mark the point where these two perpendiculars intersect as point O.
(Optional step) Repeat for the third side. This will convince you that the three bisectors do, in fact, intersect at a single point. But two are enough to find that point.
4. Done. The point O is the circumcenter of the triangle ABC. *Note:* This point may be outside the triangle. This is normal.

Note: The circumcenter is the center of a triangle's circumcircle, and the construction of the circumcircle is almost the same as this one, with the addition of the last step to actually draw the circle.

See Constructing the circumcircle of a triangle.

Try it yourself

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

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