Question 20
Let ABCD be a quadrilateral with AB parallel to CD and AB < CD. Lines AD and BC intersect at a point P. Point $ X \neq C $ on the circumcircle of triangle ABC is such that $ PC = PX $. Point $ Y \neq D $ on the circumcircle of triangle ABD is such that $ PD = PY $. Lines AX and BY intersect at Q.
Prove that PQ is parallel to AB.
Prove that PQ is parallel to AB.