ABCD is a cyclic quadrilateral such that AC bisects `angleBAD` . AD is produced to E in such a way that DE =AB . Prove that CE = CA .

If ABCD is a cyclic quadrilateral, then prove that AC.BD=AB.CD+BC.AD

ABCD is a cyclic quadrilateral. If AB = DC, then prove that AC= BD.

ABCD is a parallelogram. AB is produced to E, so that BE = AB. Prove that ED bisects BC.

ABCD is a parallelogram.AB is produced to E so that BE=AB. Prove that ED bisects BC .

ABCD is a cyclic quadrilateral in which AB and DC on being produced , meet at P such that PA = PD. Prove that AD is parallel to BC .

ABCD is a cyclic quadrilateral in which BA and CD when produced meet in E and EA = Ed. Prove that AD ||BC

ABCD is a cyclic quadrilateral in which BA and CD when produced meet in E and EA = Ed. Prove that EB = EC

In quadrilateral ABCD, AB=AD, AC bisects angleA . Prove DeltaABC~ADC .

ABCD is a cyclic quadrilateral , Sides AB and DC produced meet at point E , whereas sides BC and AD produced meet at point F. If angle DCF : angle F : angle E =3 : 5 : 4 find the angles of the cyclic quadrilateral ABCD.