körülírható

Körülírható is a geometric term used in Hungarian to describe a figure that can be circumscribed around a circle. In this sense, there exists a circle that is tangent to every side of the figure. The circle is called the incircle, and the center of all tangency points is the incenter.

This property defines what is commonly known in English as a tangential polygon. A figure that is körülírható has the tangent lengths from each vertex to the points of tangency on the two adjacent sides equal, which leads to a representation of the side lengths a_i = x_i + x_{i+1} for some positive numbers x_i.

For triangles, every triangle is körülírható; it has an incircle tangent to all three sides. The inradius r and area A relate by A = r s, where s is the semiperimeter. The incenter is the intersection of the angle bisectors.

For quadrilaterals, a convex one is körülírható if and only if the sums of opposite sides are equal: a + c = b + d. More generally, a convex polygon is tangential if there exists a circle tangent to all its sides; this is equivalent to the existence of positive tangent lengths around the polygon.

Regular polygons are examples of körülírható figures, as they possess both an incircle and a circumcircle. The concept is used in geometry and design to study shapes with uniform tangency properties.