Circumscribed Definition with Example

In Latin, circumscribe means “around” and scribere, which means to write. If you’re reminded of geometry class by circumscribing, pat yourself on the back. When two geometric figures are circumscribed, they touch but do not intersect. Watching too much TV might have been a good idea if you studied geometry, but this sounds unfamiliar to you.

There are several types of polygons, such as triangles, rectangles, regular polygons, and some other shapes, but not all polygons have circumscribes. Circumcircles or circumscribes are drawn over shapes, such as triangles and rectangles, touching all corners or vertices of the adjacent shapes. The circumcircle definition, the shapes circumscribed within another shape, and the circumcircle formulas for solving a few examples will help you better understand this concept.

Circumcircle Definition

A circle which passes through all the vertices of a polygon such as a triangle is called circumscribed. 

All cyclic polygons have a circumcircle that passes through all of their vertices or corners, and these polygons are called cyclic polygons. It is important to note, however, that not every polygon meets this criterion, only regular polygons, triangles, rectangles, and right-kites. In this circle, the circumcenter is called the center or origin of the circle, and the circumradius is called the radius of its circumcircle.

Circumcircle of Triangle

A triangle’s circumcircle is a circle passing through its three corners or vertices. In constructing a circumcircle, the center is formed by all the perpendicular bisectors of the triangle’s sides meeting. A triangle’s center can be inside or outside. A circumradius is a line segment that connects any two points of a circumcircle. Circumcircle diameter equals hypotenuse diameter for a right triangle, and origin equals midpoint hypotenuse diameter.

Circumcircle Formula

It is the same formula as a circle formula in that it calculates the area and the perimeter of the shape. If r is the radius of the circle then the area and perimeter is:

  •   Area of a circle= πr2
  • The perimeter of a circle = 2πr

Points to be noted

  • A circumcircle is also called as a circumscribed circle.
  • All quadrilaterals are not circumscribed quadrilaterals.
  • The vertices of any shape that circumscribes another shape must be connected.
  • There is a complementary relationship between an inscribed and circumscribed figure. A shape that is drawn inside another shape is called inscribed figure while a shape that is drawn outside another shape is called a circumscribed shape.  
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Azhar Ali

Azhar Ali

Mathematician and Blogger.

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