Correct option is (D) rectangle
Let parallelogram ABCD is a cyclic quadrilateral.
\(\therefore\) \(\angle B=\angle D\;\&\;\angle A=\angle C\)
\((\because\) Opposite angles in a parallelogram are equal)
Also sum of opposite angles in cyclic quadrilateral is \(180^\circ.\)
\(\therefore\) \(\angle B+\angle D=180^\circ\;and\;\angle A+\angle C=180^\circ\)
\(\Rightarrow\) \(2\angle B=180^\circ\;and\;2\angle A=180^\circ\)
\(\Rightarrow\) \(\angle B=90^\circ\;and\;\angle A=\frac{180^\circ}2=90^\circ\)
\(\therefore\) \(\angle A=\angle C=\angle B=\angle D=90^\circ\)
\(\therefore\) ABCD is a rectangle.
