Printable instructions for finding the circumcenter of a triangle with compass and straightedge or ruler

Constructing the circumcenter of a triangle

This is the step-by-step, printable version. If you PRINT this page, any ads will not be printed.

See also the animated version.

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.
Done The point O is the circumcenter of the triangle ABC. *Note:* This point may be outside the triangle. This is normal.

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.

Done The point O is the circumcenter of the triangle ABC.

Note: This point may be outside the triangle. This is normal.

Constructing the circumcenter of a triangle

Other constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions