How to construct (draw) a circle through 3 points with compass and straightedge or ruler

Circle through 3 Points

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

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.
1. (Optional*) Draw straight lines to create the line segments AB and BC. Any two pairs of the points will work.
2. Find the perpendicular bisector of one of the lines. See Constructing the Perpendicular Bisector of a Line Segment.
3. Repeat for the other line.
4. The point where these two perpendiculars intersect is the center of the circle we desire.
5. Place the compass point on the intersection of the perpendiculars and set the compass width to one of the points A,B or C. Draw a circle that will pass through all three.
6. Done. The circle drawn is the only circle that will pass through all three points.

* 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.

Try it yourself

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

Constructions pages on this site

Lines

Angles

Triangles

Triangle Centers

Circles, Arcs and Ellipses

Non-Euclidean constructions