When a parallelogram is inscribed in a circle, all its vertices lie on the circle, making it a cyclic quadrilateral. A key property of cyclic quadrilaterals is that the sum of opposite angles is 180°. In a parallelogram, opposite angles are already equal. Therefore, for a cyclic parallelogram, each angle must be 90° to satisfy the condition that their sum is 180° (since 90° + 90° = 180°). A parallelogram with all angles equal to 90° is a rectangle.

Final Answer: rectangle