

Circumcenter of a Triangle
Geometry construction using a compass and straightedge
The
circumcenter
of a triangle is the point where the
perpendicular bisectors
of the sides intersect. It is also the center of the
circumcircle,
the circle that passes through all three vertices of the triangle. This page shows how to construct (draw) the circumcenter of a triangle with compass and straightedge or ruler. This construction assumes you are already familiar with Constructing the Perpendicular Bisector of a Line Segment.
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.
Printable stepbystep instructions
The above animation is available as a
printable stepbystep instruction sheet, which can be used for making handouts
or when a computer is not available.
Proof
The image below is the final drawing above with the red labels added.
 Q.E.D
* Note
Depending where the center point lies on the bisector, there is an infinite number of circles that can satisfy this.
Two of them are shown on the right.
Steps 2 and 4 work together to reduce the possible number to just one.
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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Other constructions pages on this site
Lines
Angles
Triangles
Right triangles
Triangle Centers
Circles, Arcs and Ellipses
Polygons
NonEuclidean constructions
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