How to Draw a Circle Given Three Points

Setting up the Points

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.

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. 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.

Draw two line segments between any two sets of points. Use a straightedge to connect all of the points. For example, you might draw line segments AB and BC.

Drawing Perpendicular Bisectors

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.

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. The two arcs should intersect above and below the line.

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.

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. Extend the bisectors long enough that they intersect. The point of their intersection is the center of the circle.

Drawing the Circle

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. 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. For example, you might set the tip of the compass on the circle center, and reach the pencil to point B.

Draw the circle. Swing the compass around 360 degrees so that it draws a complete circle. The circle should pass through all three points.

Erase your guidelines. For a neat circle, make sure to erase your line segments, arcs, and perpendicular bisectors.