1. The straight line XAB cuts the circle ABZY at Aand B. The straight line XYZ cuts the circle ABZY at Y and Z. The straight line XDC cuts the circle YZCD
at D and C.Given that CZB is a straight line, prove that XAYD is a cyclic quadrilateral.
2. Triangle KLM in which the side KL has greater length than KM, ∠LKM = 90° and the bisector of ∠LKM meets LM at N. The line through N perpendicular to LM cuts KL at P and meets MK produced at Q.
(i) PKMN is a cyclic quadrilateral,
(ii) NP = NM.