12/25/2023 0 Comments Polygon superscribe![]() (In the case of the opposite angle being obtuse, drawing a line at a negative angle means going outside the triangle.) For example, for an obtuse triangle, the minimum bounding circle has the longest side as diameter and does not pass through the opposite vertex.Īlternative construction of the circumcenter (intersection of broken lines)Īn alternative method to determine the circumcenter is to draw any two lines each one departing from one of the vertices at an angle with the common side, the common angle of departure being 90° minus the angle of the opposite vertex. Even if a polygon has a circumscribed circle, it may be different from its minimum bounding circle. Every polygon has a unique minimum bounding circle, which may be constructed by a linear time algorithm. All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites are cyclic.Ī related notion is the one of a minimum bounding circle, which is the smallest circle that completely contains the polygon within it, if the circle's center is within the polygon. A polygon that does have one is called a cyclic polygon, or sometimes a concyclic polygon because its vertices are concyclic. Not every polygon has a circumscribed circle. The center of this circle is called the circumcenter and its radius is called the circumradius. In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. Circumscribed circle, C, and circumcenter, O, of a cyclic polygon, P
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