State true or false.

A cyclic parallelogram is a rectangle.

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True

False

answer is A.

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Detailed Solution

It is given a statement A cyclic parallelogram is a rectangle.
Let ABCD be a cyclic parallelogram.
Since opposite angles of a parallelogram are equal,

∠ B = ∠ D

.
In a cyclic parallelogram sum of opposites angles will be 180°. So,

\Rightarrow ∠ B + ∠ D = 180 °

\Rightarrow ∠ B + ∠ B = 180 °

\Rightarrow ∠ B = 90 °

Sum of adjacent angles of a quadrilateral equal

180 °

. So,

∠ C = 90 °

Since,

∠ A = ∠ B = ∠ C = ∠ D = 90 °

it is a rectangle.
Therefore, the given statement is true.
Hence option (1) is true.

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