Question

List the all properties of A cyclic Quadrilateral​

Answer 1

Cyclic quadrilateral:

A cyclic quadrilateral is the one which has its all vertices lying on the circumference of the circle , i.e. each of its vertices touch the outline of circle . Such quadrilateral is also called circumcircle or circumscribed circle .

If the sum of opposite pairs of angles of a quadrilateral inside a circle is 180° , the quadrilateral is called cyclic quadrilateral .

All parallelogram cannot be cyclic quadrilaterals . Some parallelogram which can be cyclic quadrilaterals are rectangle , square , trapezium .

All cyclic quadrilaterals are not parallelograms ,i.e, it is not necessary that the opposite sides should be parallel .

Properties of a cyclic quadrilateral :

• Opposite angles of cyclic quadrilateral is 180° .
• The exterior angle is equal to interior opposite angle of the quadrilateral .

In the attached figure , EBCD is a cyclic quadrilateral .

Answer 2

Step-by-step explanation:

1. Sum of opposite angles is 180º (or opposite angles of cyclic quadrilateral is supplementary)
2. Exterior angle: Exterior angle of cyclic quadrilateral is equal to opposite interior angle.
3. where s, the semiperimeter, is s = 12(a + b + c + d). This is a corollary of Bretschneider's formula for the general quadrilateral, since opposite angles are supplementary in the cyclic case. If also d = 0, the cyclic quadrilateral becomes a triangle and the formula is reduced to Heron's formula