The respective intersections E, F, G and H of the angle bisectors of angles A, B, C and D of a cyclic quadrilateral ABCD, with the circumcirle, form a rectangle.

(Drag any of the red points).

Is the result also true if ABCD becomes a crossed quadrilateral?

1) Can you explain (prove) why EFGH is a rectangle?

Hint: The result follows almost directly from a useful Lemma proved on p. 190 of my book 'Some Adventures in Euclidean Geometry' which is available as downloadable PDF or in printed bookform from Some Adventures in Euclidean Geometry.