## circumscribed polygon

### A circumscribed polygon is a polygon that has a circle drawn around it in such a way that the circle touches each vertex of the polygon

A circumscribed polygon is a polygon that has a circle drawn around it in such a way that the circle touches each vertex of the polygon. In other words, the circle is tangential to all the sides of the polygon.

To better understand this concept, let’s consider a triangle. If a circle can be drawn that just touches all three vertices of the triangle, then the triangle is circumscribed by the circle. This circle is called the circumcircle of the triangle.

Similarly, for a quadrilateral, a circle can be circumscribed around it if the circle touches all four vertices of the quadrilateral. The same concept applies to polygons with more sides as well.

The importance of circumscribed polygons lies in various geometric properties they possess. For example, if a quadrilateral is circumscribed, the sum of opposite angles is always equal to 180 degrees. Additionally, the length of the diagonal of a circumscribed quadrilateral can be found using a formula called Brahmagupta’s formula.

Circumscribed polygons are also commonly encountered in geometric constructions and proofs, as the presence of a circumscribed circle often simplifies the analysis and calculations involved.

##### More Answers:

Exploring the Properties and Formulas of Equilateral Triangles | A Comprehensive GuideUnderstanding Concentric Circles | Properties, Applications, and Mathematical Analysis

Understanding Congruent Arcs | Exploring Properties and Applications in Geometry and Circle Theorems