Prove that cyclic paralleloram must be a retangle.

Explanation

Let ABCD be a parallelogram inscribed in the circle with centre at O .
To Prove : ABCD is a rectangle .
Proof ABCD is a cyclic quadrilateral,
`thereforeangleABC+angleADC=180^(@) ` [by theorem 38]………(1)
Again ,ABCD is a parallelogram .
`thereforeangleABC=angleADC[because` opposite angles of a parallelogram are equal. ]
`therefore` from (1) we get , `angleADC+angleADC=180^(@)`
or, `2angleADC=180^(@)" or " ,angleADC=90^(@)`
Similarly , it can be proved that `angleABC=angleBCD=angleCDA=angleDAB=90^(@)`
Also , since ABCD is a parallelogram,
`thereforeAB=DCandAD=BC`.
Hence ABCD is a rectangle.