Cyclic Quadrilateral Rectangle Result

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?

Please enable Java for an interactive construction (with Cinderella).

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.

2) Can you apply or generalize the result to a cyclic hexagon? Go to Cyclic Hexagon Application & Generalization.

Created with Cinderella

Michael de Villiers, 17 January 2011.