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

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

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

Definition of Cyclic quadrilateral

Prove that the quadrilateral formed by joining the mid-points of the pairs of consecutive sides of a quadrilateral is a parallelogram.

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

Prove that the sum of the angles of a quadrilateral is 360^(@) .

Prove that, any rectangle is a cyclic quadrilateral.

Prove that, any rectangle is a cyclic quadrilateral.