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If all the 4 vertices of a quadrilateral are on a circle, then the quadrilateral is called cyclic.  The circle is circum circle.

Formula:  s = semipeimeter = 1/2 (AB+BC+CD+DA)

Area of ABCD = √[ (s - AB)(s - BC)(s - CD)(s-D) ]

Sum of opposite angles is 180 deg.

Area is also = 1/2 [ AB BC + CD DA ] Sin ABC

Figures are cyclic quadrilaterals iff  Angle ACB = angle ADB

2 3 2
If the vertices of a quadrilateral are concyclic then the quadrilateral is a cyclic quadrilateral.

The sum of the opposite angles is always equal to 180 degrees.

Area of a cyclic quadrilateral =  \sqrt{s(s-a)(s-b)(s-c)(s-d)} where a, b, c, d are sides. 

s =  \frac{a+b+c+d}{2}

Square, Rectangle, isosceles trapezium are perfect examples for cyclic quadrilaterals.