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In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius. A polygon which has a circumscribed circle is called a cyclic polygon (sometimes a concyclic polygon, because the vertices are concyclic). All regular simple polygons, isosceles trapezoids, all triangles and all rectangles are cyclic. A related notion is the one of a minimum bounding circle, which is the smallest circle that completely contains the polygon within it. Not every polygon has a circumscribed circle, as the vertices of a polygon do not need to all lie on a circle, but every polygon has a unique minimum bounding circle, which may be constructed by a linear time algorithm. Even if a polygon has a circumscribed circle, it may not coincide with its minimum bounding circle; for example, for an obtuse triangle, the minimum bounding circle has the longest side as diameter and does not pass through the opposite vertex. ==Triangles== All triangles are cyclic, i.e. every triangle has a circumscribed circle. This can be proven on the grounds that the general equation for a circle with center (''a'', ''b'') and radius ''r'' in the Cartesian coordinate system is : Since this equation has three parameters (''a'', ''b'', ''r'') only three points' coordinate pairs are required to determine the equation of a circle. Since a triangle is defined by its three vertices, and exactly three points are required to determine a circle, every triangle can be circumscribed. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「circumscribed circle」の詳細全文を読む スポンサード リンク
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