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Constructing the circumcircle 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.

Geometry construction with compass and straightedge or ruler or ruler
1.  Find the bisector of one of the triangle sides. Any one will do. See Constructing the Perpendicular Bisector of a Line Segment. Geometry construction with compass and straightedge or ruler or ruler
2.  Repeat for the another side. Any one will do. Geometry construction with compass and straightedge or ruler or ruler
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.
3.  The point where these two perpendiculars intersect is the triangle's circumcenter, the center of the circle we desire.   Note: This point may lie outside the triangle. This is normal. Geometry construction with compass and straightedge or ruler or ruler
4.  Place the compasses' point on the intersection of the perpendiculars and set the compasses' width to one of the points A,B or C. Draw a circle that will pass through all three. Geometry construction with compass and straightedge or ruler or ruler
5.  Done. The circle drawn is the triangle's circumcircle, the only circle that will pass through all three of its vertices. Geometry construction with compass and straightedge or ruler or ruler

Other constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions