
Circle through 3 Points
Geometry construction using a compass and straightedge
Given three points, it is possible to draw a circle that passes through all three*. This page shows how to construct (draw) a circle through 3 given points with compass and straightedge or ruler. It works by joining two pairs of points to create two
chords.
The perpendicular bisectors
of a chords always passes through the center of the circle. By this method we find the center and can then draw the circle.
This is virtually the same as
constructing the circumcircle a triangle.
If you draw three lines linking the given points, you will get a triangle.
The
circumcircle
passes through all three
vertices, just as here.
* What if the points are collinear?
If the three points are
collinear (all lying on a straight line)
then the circle passing through all three will have a radius of infinity.
So there is no practical circle that can pass through three collinear points.
If you tried the construction, you would find that the two radii (JO, LO) would be parallel and so never meet at a center.
In the language of mathematics, we might say they do intersect, but at infinity.
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 items 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 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.
Other constructions pages on this site
Lines
Angles
Triangles
Right triangles
Triangle Centers
Circles, Arcs and Ellipses
Polygons
NonEuclidean constructions
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