Omkredscirkel

Omkredscirkel refers to the circumcircle of a polygon, which is a circle that passes through all the vertices of the polygon. For a triangle, the circumcircle always exists and is unique. Its center, known as the circumcenter, is the point where the perpendicular bisectors of the triangle's sides intersect. The radius of the circumcircle is called the circumradius.

Not all polygons have a circumcircle. A polygon for which a circumcircle exists is called a cyclic polygon. For example, all triangles are cyclic. Quadrilaterals that are cyclic are known as cyclic quadrilaterals, and they have specific properties, such as opposite angles summing to 180 degrees. Regular polygons are always cyclic.

The circumcircle plays a role in various geometric theorems and calculations. For instance, the area of a triangle can be expressed in terms of its side lengths and the circumradius. The concept of a circumcircle is fundamental in Euclidean geometry and has applications in fields like trigonometry and computational geometry.