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A circle is defined by any three non-collinear points. [1] X 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.
Steps
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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.
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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] X Research source
- 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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Draw two line segments between any two sets of points. Use a straightedge to connect all of the points. [3] X Research source
- For example, you might draw line segments AB and BC.
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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] X Research source
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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] X Research source
- The two arcs should intersect above and below the line.
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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] X Research source
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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] X Research source Extend the bisectors long enough that they intersect. The point of their intersection is the center of the circle. [8] X Research source
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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] X 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] X Research source
- For example, you might set the tip of the compass on the circle center, and reach the pencil to point B.
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Draw the circle. Swing the compass around 360 degrees so that it draws a complete circle. The circle should pass through all three points.
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Erase your guidelines. For a neat circle, make sure to erase your line segments, arcs, and perpendicular bisectors.
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References
- ↑ https://www.khanacademy.org/math/geometry-home/triangle-properties/perpendicular-bisectors/v/three-points-defining-a-circle
- ↑ http://jwilson.coe.uga.edu/EMAT6680Su06/Byrd/Assignment%20Nine/CyclicQuad.pdf
- ↑ http://www.mathopenref.com/const3pointcircle.html
- ↑ http://www.virtualnerd.com/geometry/triangle-relationships/perpendicular-angle-bisectors/construct-perpendicular-bisector-example
- ↑ https://www.mathsisfun.com/geometry/construct-linebisect.html
- ↑ http://www.virtualnerd.com/geometry/triangle-relationships/perpendicular-angle-bisectors/construct-perpendicular-bisector-example
- ↑ http://www.mathopenref.com/const3pointcircle.html
- ↑ https://www.khanacademy.org/math/geometry-home/triangle-properties/perpendicular-bisectors/v/three-points-defining-a-circle
- ↑ http://www.coolmath.com/reference/circles-geometry
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