Assume that ABCD is a cyclic parallelogram (a parallelogram inscribed in a circle). We need to prove that ABCD is a rectangle. Proof: Since ABCD is a parallelogram, \[ \angle ABC = \angle ADC \] Also, since ABCD is a cyclic quadrilateral, \[ \angle ABC + \angle ADC = 180^\circ \] So, \[ 2\angle ABC = 180^\circ \Rightarrow \angle ABC = 90^\circ \] Since one angle of the parallelogram is a right angle, ā“ ABCD is a rectangle. (Proved)