Prove that a cyclic parallelogram is a rectangle.
Solution:
It is given that parallelogram ABCD is cyclic. We need to prove that ABCD is a rectangle.
(Opposite angles of a parallelogram are equal) (1)
(2)
(Sum of opposite angles of a cyclic quadrilateral is equal to
)
Using equation (1) in equation (2), we get
(3)
Therefore, ABCD is a parallelogram with
which means that ABCD is a rectangle.
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