Question

prove that a 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

Since we know that opposite angles of a parallelogram are equal and the sum of opposite angles of a cyclic parallelogram is 180°

Therefore all angles will be of 90°.

Hence it is a rectangle.