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Cyclic Quadrilateral : - A quadrilateral whose all the four vertices lie on a circle is called cyclic quadrilateral.

Theorem – 4 The opposite angles of a cyclic quadrilateral are supplementary.

Given : A cyclic quadrilateral ABCD whose vertices lie on a circle with centre 0.

To Prove :

Construction : OB and OD are joined.

Proof :

Statement	Reason
1.	1. Angle at the circumference = 1/2 angle at the centre
2.	2. Reason (1)
3.	3. Statement (1) & (2) ref

Corolary : If a side of a cyclic quadrilateral is produced, the exterior angle is equal to the interior opposite angle.

Given : Side AB of a cyclic quadrilateral is produced to E.

To Prove :

Proof :

Statement	Reason
1.	1. Linear Pair
2.	2. Opposite angles of a cyclic quadrilateral
3.	3. Statements (1) & (2)
4.	4. Statement (3)