How to Circumscribe a Circle
A circumscribed circle, also referred to as a "circumcircle," is a circle containing all three of the vertices of a triangle. The center of a triangle is called a "circumcenter"---also the center of the circumcircle. Locate the circumcenter iin order to circumscribe a circle around the triangle---a simple task you can perform with a compass, ruler and a pencil.
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Instructions
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Draw a triangle on a sheet of paper with a pencil.
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Place the point of the compass on one of the vertices of the triangle. Set the width of the compass to about 2/3 of the length of the side of the triangle. Hold the point of the compass on the vertex and draw an arc on each side of the triangle. Place the point of the compass on the next vertex to the right, and draw an arc on the sides of the triangle across the first set of arcs. Place the ruler on the center points of the arcs, and draw a line from point to point.
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Place the point of the compass on the second vertex used. Set the width of the compass to about 2/3 of the length of the side of the triangle. Hold the point of the compass on the vertex, and draw an arc on the side of the triangle and in the center of the triangle. Place the point of the compass on the next vertex on the right, and draw an arc on the side and in the center of the triangle across the first set of arcs. Place the ruler on the center points of the arcs, and draw a line from point to point. The point where the lines intersect in the center of the triangle becomes the circumcenter.
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Place the point of the compass on the circumcenter. Place the other side of the compass on the third vertex. Draw a circle around the triangle with the compass. You have now circumscribed a circle around a triangle.
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References
- Math Open Reference: Circumcircle of a Triangle
- Math is Fun: Circumscribe a Circle on a Triangle
- Northern Virginia Community College: To Circumscribe a Circle About a Given Triangle
- Calvin College: Circumscribed Circles, Inscribed Circles, and Escribed Circles
- Math Open Reference: Perpendicular Bisector of a Line Segment
- Photo Credit compass image by Sid Viswakumar from Fotolia.com
