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