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.

 

Subjects Maths (Part-1) by Mr. M. P. Keshari
Chapter 9 Circle
Chapter 10 Tangents to a circle
Chapter 11 Geometrical Construction
Chapter 12 Troigonometry
Chapter 13 Height and Distance
Chapter 14 Mensuration
Chapter 15 Statistics
Chapter 16 Probability
Chapter 17 Co-ordinate Geometry