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?
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.