Episode 2000
Circumscribed circle
Tue, 2022-Oct-25 00:55 UTC
Length - 1:55
Direct Link
Welcome to random Wiki of the Day where we read the summary of a random Wikipedia page every day.
The random article for Tuesday, 25 October 2022 is Circumscribed circle.
In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius.
Not every polygon has a circumscribed circle. A polygon that does have one is called a cyclic polygon, or sometimes a concyclic polygon because its vertices are concyclic. All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites 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, if the circle's center is within the polygon. 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 be different from 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.
This recording reflects the Wikipedia text as of 00:55 UTC on Tuesday, 25 October 2022.
For the full current version of the article, see Circumscribed circle on Wikipedia.
This podcast is produced by Abulsme Productions based on Wikipedia content and is released under a Creative Commons Attribution-ShareAlike License.
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This has been Kajal Neural. Thank you for listening to random Wiki of the Day.
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