The quadrilateral formed by angle bisectors of a cyclic quadrilateral is also cyclic.

Definition of Cyclic quadrilateral

The quadrilateral formed by the bisectors of the angles of a parallelogram is a

Prove that the quadrilateral formed (if possible by the internal angle bisectors of any quadrilateral is cyclic

Prove that, any rectangle is a cyclic quadrilateral.

Prove that, any rectangle is a cyclic quadrilateral.

Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle.

ABCD is a cyclic quadrilateral (see Figure). Find the angles of the cyclic quadrilateral.

The bisectors of the angles formed by producing the opposite sides of a cyclic quadrilateral (provided that they are not parallel) intersect at right angle.