Problem 3

Let point P lie on a side AB of ΔABC. Circle C(A) is the circumcircle of ΔAPC. Circle(B) is the circumcircle of ΔBPC. Q is an arbitrary point on the segment AB. Points A' on C(B) and B' on C(A) lie on the same side of AB as C such that QA'||AC and QB'||BC. Show that
  1. Quadrilateral PQA'B' is cyclic and
  2. Points A', C', B' are collinear.


One solution appears elsewhere.