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?

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

If stuck, read my paper An interesting cyclic quadrilateral result.

Created with Cinderella

Michael de Villiers, 16 May 2011.