Cyclic Quadrilateral Formula

There are various formulas given for Cyclic Quadrilateral, some of the important ones are:

• Area of Cyclic Quadrilateral
• Radius of Circumcircle
• Diagonals of Cyclic Quadrilateral

Let’s discuss these formula in detail as follows:

Area of Cyclic Quadrilateral Formula

Area of the cyclic quadrilateral is calculated using the following formula:

Area of Cyclic Quadrilateral = √(s-a)(s-b)(s-c)(s-d)

Where,

• a, b, c, d are the sides of Cyclic Quadrilateral, and
• s is semi perimeter [s = (a + b + c + d) / 2].

Note: This formula is also known as Brahmagupta’s Formula.

Radius of Circumcircle

Let the sides of  a cyclic quadrilateral be a, b, c and d, and s is the semi perimeter, then the radius of circumcircle is given by,

R = 1/4 [Tex]\bold{\sqrt{\frac{(ab + cd)(ac + bd)(ad + bc)}{(s-a)(s-b)(s-c)(s-d)}}}[/Tex]

Diagonals of Cyclic Quadrilaterals

Diagonal is the line in any polygon which joins any two non-adjacent vertices.

Suppose a, b, c and d are the sides of a cyclic quadrilateral and p & q are the diagonals, then we can find the diagonals of it using the below-given formulas:

p = [Tex]\bold{\sqrt{\frac{(ac + bd)(ad + bc)}{ab + cd}}}[/Tex] and q = [Tex]\bold{\sqrt{\frac{(ac + bd)(ab + cd)}{ad + bc}}}[/Tex]

Cyclic Quadrilateral is a special type of quadrilateral in which all the vertices of the quadrilateral lie on the circumference of a circle. In other words, if you draw a quadrilateral and then find a circle that passes through all four vertices of that quadrilateral, then that quadrilateral is called a cyclic quadrilateral.

Cyclic Quadrilaterals have several interesting properties, such as the relationship between their opposite angles, the relationship between their diagonals, and Ptolemy’s theorem. We will learn all about the Cyclic Quadrilateral and its properties in this article.