Question

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.
Prove that
   (i) PKMN is a cyclic quadrilateral,
  (ii) NP = NM.

Answer 1

these are really hard questions. can you ask simpler questions?