# What is cyclic property?

## What is cyclic property?

If all four points of a quadrilateral are on circle then it is called cyclic Quadrilateral. A quadrilateral PQRS is said to be cyclic quadrilateral if there exists a circle passing through all its four vertices P, Q, R and S. Let a cyclic quadrilateral be such that. PQ = a, QR = b, RS = c and SP = d.

## What is S in brahmagupta’s formula?

S = \sqrt{(s – a)(s – b)(s – c)(s – d)}, where s is the semiperimeter of the quadrilateral: s = (a + b + c + d)/2.

What is the formula of area of quadrilateral?

Hence, the formula to find the area of the quadrilateral is derived as: Area of General Quadrilateral Formula = 1/2 x diagonals length x ( sum of the height of two triangles ).

How do you use Ptolemy’s Theorem?

In a quadrilateral, if the sum of the products of the lengths of its two pairs of opposite sides is equal to the product of the lengths of its diagonals, then the quadrilateral can be inscribed in a circle i.e. it is a cyclic quadrilateral.

### What does Concyclic mean?

Definition of concyclic 1 : lying on one and the same circle —used of a system of points. 2 : cut in circles by the same parallel planes —used of certain systems of quadrics.

### How do you prove Concyclic?

Proving Concyclic Points

1. Finding the product of the lengths of the diagonals of the quadrilateral formed by the points.
2. Finding the sum of the products of the measures of the pairs of opposite sides of the quadrilateral formed by the points.
3. If these two values are equal, the points are concyclic.

Who discovered Euclidean geometry?

Greek mathematician Euclid
Euclidean geometry, the study of plane and solid figures on the basis of axioms and theorems employed by the Greek mathematician Euclid (c. 300 bce). In its rough outline, Euclidean geometry is the plane and solid geometry commonly taught in secondary schools.

How do you use Brahmagupta’s formula?

Some Examples Use Brahmagupta’s formula to calculate the area of a square with sides each equal to 6 inches. The expected answer is A = 62 = 36 square inches. S = (a + b + c + d)/2 = (6 + 6 + 6 + 6)/2 = 24/2 = 12.

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