Cyclic quadrilateral

Class IX

Prepared by P.E.Venugopalan K.V.KELTRON NAGAR

Cyclic quadrilateral

A quadrilateral is called a cyclic quadrilateral if all the four vertices of it lie on a circle

Theorem (10.11)

The sum of either pair of opposite angles of a cyclic quadrilateral is 180°

D

C

B

A

If ABCD is a cyclic quadrilateral ,then

(i) ∟A + ∟C =180°

and

(ii) ∟B + ∟D = 180°

Converse of Theorem 10.11

If the sum of a pair of opposite angles of a quadrilateral is 180°,the quadrilateral is cyclic(Theorem 10.12)

A

D

C

BABCD is a cyclic quadrilateral if

(i) ∟A + ∟C =180°

Or

(ii) ∟B + ∟D = 180°