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

Explanation

To prove that the quadrilateral formed by the internal angle bisectors of any quadrilateral is cyclic, we will follow these steps:

### Step 1: Define the Quadrilateral and Its Angle Bisectors
Let ABCD be any quadrilateral. The internal angle bisectors of angles A, B, C, and D intersect at points E, F, G, and H respectively. Thus, we have:
- E is the intersection of the angle bisectors of angles A and B.
- F is the intersection of the angle bisectors of angles B and C.
- G is the intersection of the angle bisectors of angles C and D.
- H is the intersection of the angle bisectors of angles D and A.
...