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.
* 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.


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 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. 

6. Done. The circle drawn is the only circle that will pass through all three points. 
