Circumcircle of a Triangle
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.
This construction assumes you are familiar with Constructing the Perpendicular Bisector of a Line Segment.
Instructions Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping.
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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.
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