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## 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:

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

2019-12-06