ABCD is a cyclic quadrilateral. A circle passing through A and B meet AD and BC in points E and F respectively prove that EF is parallel to DC.
ABFE is a cyclic quadrilateral.
Opposite angles of a cyclic quadrilateral are supplementary.
x + y = 180°
Also,
x + z = 180°
x + y = x + z
y = z
As these are corresponding angles EF is parallel to DC.