## How do you find the area of a quadrilateral in a circle?

Example: In a circular grassy plot, a quadrilateral shape with its corners touching the boundary of the plot is to be paved with bricks. Find the area of the quadrilateral when the sides of the quadrilateral are 36 m, 77 m, 75 m and 40 m. The area of the cyclic quadrilateral =√78×37×39×74=39×37×2=2886 square meters.

## What is a quadrilateral that is inscribed within a circle?

In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic.

**How do you find the perimeter of a quadrilateral inscribed in a circle?**

The perimeter of a quadrilateral is equal to the sum of its four sides. i.e., the perimeter of a quadrilateral ABCD is AB + BC + CD + DA.

### How do you know if a quadrilateral can be inscribed in a circle?

A quadrilateral is said to be inscribed in a circle if all four vertices of the quadrilateral lie on the circle. A quadrilateral is cyclic if and only if its opposite angles are supplementary.

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

Yes, a parallelogram, in particular, a square, cabe inscribed inside of a circle. More generally, any regular polygon can be inscribed of a circle, and a circle can actually be realized as the geometric limit of an n-sided regular polygon as n approaches infinity.

**Can a circle be circumscribed about the quadrilateral?**

A cyclic quadrilateral is a quadrilateral for which a circle can be circumscribed so that it touches each polygon vertex. A quadrilateral that can be both inscribed and circumscribed on some pair of circles is known as a bicentric quadrilateral .

#### What is the opposite of a quadrilateral?

In a square, rectangle, or rhombus, the opposite side lines are parallel. A quadrilateral with the opposite side lines parallel is known as a parallelogram. If only one pair of opposite sides is required to be parallel, the shape is a trapezoid.

#### What are the angles in a quadrilateral?

The maximum angle is 360°. This is the angle all the way round a point. Half of this is the angle on a straight line, which is 180°. A quadrilateral is any four-sided shape. These shapes also have exactly 4 interior angles. The sum of the interior angles of a quadrilateral are equal to 360°.