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Circumcircle of a Triangle
Click here for a printable triangle circumcircle worksheet
How to construct the
circumcircle of a
triangle. (Also known as circumscribed circle).
We start with a given triangle ABC, and end with the circle that passes through all three of its vertices.
Note: This is almost identical to the construction of a circle through three points.
In this case the three points are already joined by lines,
but aside from that, the constructions are the same.
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 |
Find the bisector
of one of the triangle sides. Any one will do. See
Constructing the Perpendicular Bisector of a Line Segment. |
| Step 2 |
Repeat for the another side. Any one will do. |
| Step 3 |
The point where these two perpendiculars intersect is the triangle's circumcenter, the center of the circle we desire.
Note: This point may lie outside the triangle. This is normal.
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| Step 4 |
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 5 |
Done. The circle drawn is the triangle's circumcircle, the only circle that will pass through all three of it's vertices. |
Try it yourself
Click here for a printable worksheet containing two triangle circumcircle problems.
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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