This construction assumes you are already familiar with Constructing the Perpendicular Bisector of a Line Segment.
| After doing this | Your work should look like this |
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We start with a triangle ABC. |
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| 1. Find the bisector of one of the triangle sides. Any one will do. See Constructing the Perpendicular Bisector of a Line Segment. | ![]() |
| 2. Repeat for the another side. Any one will do. | ![]() |
| Optional step. Repeat for the third side. This will convince you that the three bisectors do, in fact, intersect at a single point. But two are enough to find that point. | |
| 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. | ![]() |
| 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. | ![]() |
| 5. Done. The circle drawn is the triangle's circumcircle, the only circle that will pass through all three of its vertices. | ![]() |