Chapter 9 : Circle

Cyclic Quadrilaeral

Quadrilateral whose all the (four) vertius lie on a circle is called a cyclic quadrilateral.

Theorem 4:- The sum of the either pair of the opposite angle of a cyclic quadrilateral is 180⁰

Give: - A cyclic quadrilateral ABCD

To prove:-

Construction:- Let O be the centre of the circle passing through A, B, C and D. OB and OD are joined.

Proof:-

                = x/2, say                 (Theo.2)

and

                         = y/2, say       (Theo.2)

Adding (i) and (ii) we get

As the sum of the angles of a quadrilateral is 360⁰, there fore,

Example 6. In the adjoining figure,

Solution:- As BD = DC

ABCD is a cyclic quadrilateral.