Circumcircle of a Polygon
Definition: The circle that passes through each
of the regular polygon.
Also - circumscribed circle.
Adjust the polygon below by dragging any orange dot, or alter the number of sides. Note the behavior of the polygon's circumcircle.
For Regular Polygons
The circumcircle of a regular polygon
is the circle that passes through every vertex of the polygon.
If the number of sides is 3, then the result is an
equilateral triangle and its circumcircle is exactly
the same as the one described in Circumcircle of a Triangle.
Finding the radius
The radius of the circumcircle (the circumradius) of a regular polygon is exactly the same as the radius of the polygon.
For more on the radius and formulas to calculate it see Radius of a Polygon.
Irregular polygons are not usually considered as having a circumcircle. If you draw a polygon at random,
it is unlikely there will be a circle that passes through every vertex.
An alternative view
Sometimes you may see an alternative definition of the circumcircle:
"the smallest circle that will enclose the polygon"
For this definition it is possible for an irregular polygon to have a circumcircle,
since the circle need not pass through every vertex, as shown on the right.
Related polygon topics
Types of polygon
Area of various polygon types
Perimeter of various polygon types
Angles associated with polygons
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