How to Draw a Circle Given Three Points

Co-authored by wikiHow Staff

Last Updated: March 3, 2021 References

A circle is defined by any three non-collinear points.^{[1]
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Research source} This means that, given any three points that are not on the same line, you can draw a circle that passes through them. It is possible to construct this circle using only a compass and straightedge.

Part 1

Part 1 of 3:

Setting up the Points

1
Draw your three points. If you have the coordinates of the points, map them on a coordinate plane. If you are not working with specific points, you can draw your own on a piece of paper.
- For example, you might draw points A, B, and C in any position you'd like.
2
Determine whether your points are noncollinear. Noncollinear means that they are not on the same line. You can draw a circle from any three points, as long as they are not on the same line.^{[2]
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- If you aren’t sure whether the points are collinear, lay a straightedge across them. If the straightedge passes through all three points, the points are collinear, and you cannot use them to draw a circle.
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3
Draw two line segments between any two sets of points. Use a straightedge to connect all of the points.^{[3]
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- For example, you might draw line segments AB and BC.

Part 2

Part 2 of 3:

Drawing Perpendicular Bisectors

1
Draw an arc centered at the first endpoint of the first line segment. To do this, place the compass tip on the first endpoint. Open the compass to a little more than halfway across the line segment. Draw an arc across the line segment.^{[4]
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2
Draw an arc centered at the second endpoint. Without changing the width of the compass, place the compass tip on the second endpoint. Draw a second arc across the line segment.^{[5]
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- The two arcs should intersect above and below the line.
3
Draw a line connecting the intersections of the arc. Line up a straightedge with the intersection of the arcs above the line, and the intersection of the arcs below the line. Draw a line connecting these two points. The line you draw is a perpendicular bisector. It bisects the line at a right angle.^{[6]
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4
Draw the perpendicular bisector of the second line segment. Use a compass and straightedge to construct the bisectors as you did with the first line segment.^{[7]
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Research source} Extend the bisectors long enough that they intersect. The point of their intersection is the center of the circle.^{[8]
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Part 3

Part 3 of 3:

Drawing the Circle

1
Set the compass width to the circle’s radius. The radius of a circle is the distance from the center to any point on the circle’s edge.^{[9]
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Research source} To set the width, place the tip of the compass on the center of the circle, and open the compass to any one of your original points.^{[10]
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- For example, you might set the tip of the compass on the circle center, and reach the pencil to point B.
2
Draw the circle. Swing the compass around 360 degrees so that it draws a complete circle. The circle should pass through all three points.
3
Erase your guidelines. For a neat circle, make sure to erase your line segments, arcs, and perpendicular bisectors.