Let ABCD be a circumscribed quadrilateral, assume ABCD is not a kite. Denote the circumcenters of triangle ABC,BCD,CDA,DAB by OD,OA,OB,OC respectively.
a. Prove that OAOBOCOD is circumscribed.
b. Let the angle bisector of ∠BAD intersect the angle bisector of ∠OBOAOD in X. Similarly define the points Y,Z,W. Denote the incenters of ABCD,OAOBOCOD by I,J respectively. Express the angles ∠ZYJ,∠XYI in terms of angles of quadrilateral ABCD. geometrycircumcircleangle bisectorincenter