CYCLIC POLYGON Meaning and
Definition
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A cyclic polygon is a polygon with vertices that all lie on the circumference of a common circle. The term "cyclic" refers to the property that all the vertices are located on the same curve. The circle containing all the vertices of the polygon is called the circumcircle of the cyclic polygon.
To qualify as a cyclic polygon, all of its vertices must be part of the circumcircle. This means that if a polygon has n sides, then it must have exactly n vertices lying on the circumference of the circle. Additionally, it must have a circumcenter, which is the center point of the circumcircle.
One characteristic of cyclic polygons is that their opposite angles are supplementary, meaning they add up to 180 degrees. This property arises from the fact that each vertex of the polygon forms an angle with the center of the circumcircle. As a result, the sum of the interior angles of a cyclic polygon is equal to (n-2) times 180 degrees, where n represents the number of sides.
Cyclic polygons have several notable properties that set them apart from non-cyclic polygons. For instance, their circumcircle allows for various geometric constructions and calculations. This property makes them particularly relevant in areas such as geometry, trigonometry, and computational mathematics.
Overall, a cyclic polygon is a geometric shape defined by its vertices lying on the circumference of a common circle, contributing to its distinct properties and applications.
Etymology of CYCLIC POLYGON
The word "cyclic" derives from the Greek word "kuklos" (κύκλος), meaning "circle" or "ring". It is commonly used in mathematics to describe an object or shape that belongs to or relates to a circle.
The word "polygon" comes from the Greek words "poly" (πολύ), meaning "many", and "gonía" (γωνία), meaning "angle". It refers to a closed geometric figure with straight sides, consisting of multiple angles.
Therefore, a "cyclic polygon" can be understood as a polygon that can be inscribed in or circumscribed around a circle, i.e., all its vertices lie on the circumference of a circle.
