Verify that rectangle is the only parallelogram that can be inscribed in a circle.
Proof:
Given that, \(ABCD\) is a cyclic parallelogram.
Therefore, \(∠A+∠C=\)\(^°\) []
\(∠A=∠\) []
Therefore, \(∠A=∠C=\)\(=\)\(^°\)
Similarly, \(∠B+∠D=\)\(^\circ\)
\(∠B=∠\) []
\(∠B=∠D =\)\(=\)\(^°\) [opposite of a parallelogram]
Each angle of \(ABCD\) is \(90^°\)
Since, opposite sides are parallel and all the angles are \(90^\circ\), \(ABCD\) is a rectangle.