## 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?

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.