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Constructing a circle through 3 given points

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See also the animated version.

After doing this Your work should look like this

We start with three given points. We will construct a circle that passes through all three.

Geometry construction with compass and straightedge or ruler or ruler

1.  (Optional*) Draw straight lines to create the line segments AB and BC. Any two pairs of the points will work.

* We draw the two lines to make it clear when we later draw their perpendicular bisectors, but it is not strictly necessary for them to actually be there to do this.

Geometry construction with compass and straightedge or ruler or ruler
2.  Find the perpendicular bisector of one of the lines. See Constructing the Perpendicular Bisector of a Line Segment. Geometry construction with compass and straightedge or ruler or ruler
3.  Repeat for the other line. Geometry construction with compass and straightedge or ruler or ruler
4.  The point where these two perpendiculars intersect is the center of the circle we desire. Geometry construction with compass and straightedge or ruler or ruler
5.  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
6.  Done. The circle drawn is the only circle that will pass through all three points. 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