Properties of Circles Part 3

Cyclic Quadrilaterals

A quadrilateral with its four vertices lying on the circumference of a circle is called a cyclic quadrilateral.



Property 1

In a cyclic quadrilateral, the opposite angles are supplementary,

Proof:

Cyclic Quadrilaterals

Let b = 50

2d = 360 - 100 = 260
d = 260/2 = 30
b + d = 30 + 50 = 180.

Property 2

If one side of a cyclic quadrilateral is produced, the exterior angle so formed is equal to the interior angle.

Proof


b + d = 180°(opp. angles of cyclic quad.)
x + d = 180°(adj. angles on a str. l)
b + d = x + d
b = x
angle ABC = angle CDE