Prove that the bisectors of the 4 interior angles of a quadrilateral form a cyclic quadrilateral. I can't seem to draw a good diagram for this question. I tried to draw a quadrilateral and draw the angle bisectors, but they intersected to form a very small quadrilateral. Then I tried to draw a cyclic quadrilateral and extend the sides to form an external quadrilateral, but the diagram turned out shoddy. A diagram and perhaps a starting point hint would be greatly appreciated!

You don't need a nice diagram, a lousy one will do just as well ![enter image description here](

Let the angles of the original quadrilateral be $2\alpha,2\beta,2\gamma,2\delta$ so that $$\alpha+\beta+\gamma+\delta=180$$

So according to the diagram, the opposite angles in the small quadrilateral add to $180$