ABCD is a cyclic quadrilateral. AB and DC produced meet at point P. Which of the following statements is/are correct? I. △PAD is similar to △PBC. II. ∠PAD + ∠PDA = ∠PBC + ∠PCB

Since ABCD is cyclic, ∠PAD = 180° − ∠BAD = ∠BCD (exterior angle of cyclic quadrilateral equals opposite interior angle). Also ∠P is common to both triangles PAD and PBC. So by AA similarity, △PAD ~ △PBC. So I is correct. Since the triangles are similar, corresponding angles are equal: ∠PAD = ∠PCB and ∠PDA = ∠PBC. Therefore ∠PAD + ∠PDA = ∠PCB + ∠PBC. So II is also correct.