Question

TPT every cyclic parallelogram is a rectangle

Answer 1

Opposite angles in a parallelogram are congruent, while opposite angles in a cyclic quadrilateral are supplementary.

Congruent supplementary angles are right angles, so opposite angles in a cyclic parallelogram are right angles. Thus all four angles are right angles, and it's a rectangle.

Answer 2

Any parallelogram cannot be cyclic. For any quadrilateral to be cyclic the sum of the opposite angles should be 180 deg. So the quadrilaterals that can be cyclic are definitely a square and a rectangle.

Every rectangle, including the special case of a square, is a cyclic quadrilateral because a circle can be drawn around it touching all four vertices.