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,
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