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A Circle Through 3 Points
Click here for a printable worksheet for this construction
This shows how to construct a circle that passes through three given points.
We start with the three points A,B and C, and end with a circle O that passes through all three.
Instructions 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
| Step 1 |
Draw straight lines to create the line segments AB and BC. Any two pairs of the points will work. |
| Step 2 |
Find the bisector
of one of the lines. See
Constructing the Perpendicular Bisector of a Line Segment. |
| Step 3 |
Repeat for the other line. |
| Step 4 |
The point where these two perpendiculars intersect is the center of the circle we desire. |
| Step 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. |
| Step 6 |
Done. The circle drawn is the only circle that will pass through all three points. |
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
Lines
Angles
Triangles
Triangle Centers
Circles, Arcs and Ellipses
Non-Euclidean constructions
(C) 2007 Copyright John Page
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