Characterizations of Cyclic Quadrilaterals Let ABCD be a convex quadrilateral,and let M be the intersection of its diagonals AC and BD.Suppose the sides BA and CD,when extended,in- tersect,say at H.Then ABCD is cyclic if and only if any one of the following conditions holds: 1.BAC=BDC 2.A+C=180i.e.DAB+ZDCB=180 3.HDA=HBC 4.AMMC=BMMD 5.HAHB=HDHC Proof. I will do in class