A quadrilateral ABCD is called cyclic if all the four vertices
of it lie on a circle (see Fig 1).
Here we find that and .
Theorems related to Cyclic Quadrilateral are mentioned below.
Theorem 1: The sum of either pair of opposite angles of a cyclic quadrilateral
is .
Theorem 2: If the sum of a pair of opposite angles of a quadrilateral is ,
the quadrilateral is cyclic.
Examples
1: In Fig 2, is a cyclic quadrilateral in which and are its diagonals.
If and , find
Solution:
(Angles in the same segment)
Therefore,
But (Opposite angles of a cyclic quadrilateral)