# Which polygons can have circumscribed circles?

Table of Contents

## Which polygons can have circumscribed circles?

Not every polygon has a circumscribed circle. A polygon that does have one is called a cyclic polygon, or sometimes a concyclic polygon because its vertices are concyclic. All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites are cyclic.

## What shapes Cannot be inscribed in a circle?

Some quadrilaterals, like an oblong rectangle, can be inscribed in a circle, but cannot circumscribe a circle. Other quadrilaterals, like a slanted rhombus, circumscribe a circle, but cannot be inscribed in a circle.

## Can a rhombus always be inscribed in a circle?

Not any rhombus can be inscribed in a circle. In general a rhombus has two diagonals that are not equal (except a square) and therefore the endpoints of the shorter diagonal would not be points on the circle. Unless the rhombus is a square, it can’t be inscribed in a circle.

## What does it mean if a shape is inscribed in a circle?

In geometry, an inscribed planar shape or solid is one that is enclosed by and “fits snugly” inside another geometric shape or solid. A polygon inscribed in a circle is said to be a cyclic polygon, and the circle is said to be its circumscribed circle or circumcircle.

## What is a filled circle called?

word-request mathematics terminology. When talking about circles, a “circle” refers merely to a line in the shape of a circle, whereas “disk” (or “disc”) refers to a “filled circle”.

## What is the formula of inscribed circle?

When a circle is inscribed in a square, the length of each side of the square is equal to the diameter of the circle. That is, the diameter of the inscribed circle is 8 units and therefore the radius is 4 units. The area of a circle of radius r units is A=πr2 . Substitute r=4 in the formula.

## What is the formula to find the Circumcenter?

Steps to find the circumcenter of a triangle are:

- Calculate the midpoint of given coordinates, i.e. midpoints of AB, AC, and BC.
- Calculate the slope of the particular line.
- By using the midpoint and the slope, find out the equation of the line (y-y1) = m (x-x1)
- Find out the equation of the other line in a similar manner.