Six points A,B,C,D,E and F lie on a circle, with AB||ED and AF||CD.
Prove that BC||EF.
Hints: Draw the lines AD, BE, CF. Look at all the angles between these lines and the sides of the hexagon ABCDEF, mark all those that are equal to each other. (You should find three other angles that are the same as the angle BAD, and three other angles that are the same as the angle FAD. Also, find an angle equal to EBC, and an angle equal to BCF.) Then use the fact that opposite angles of a cyclic quadrilateral are supplementary.