Hint: Join AB. Label angle CAB as angle , then find angles EAB, CDB and EFB all in terms of . You will need to use the fact that the opposite angles of a cyclic quadrilateral add up to 180 and if you are not sure why then see the article on Cyclic Quadrilaterals. What did you notice about the line segments CD and EF? By considering two of these angles can you now prove what your eyes told you about CD and EF?

The following solution was sent by `kevin295' of whom we hope to have further identification soon.

The segments CD and EF are parallel.

PROOF:

ABDC is a cyclic quadrilateral, therefore
angle CDB + angle CAB=180 ..............(1)

Angle CAB and angle BAE are adjacent angles on a straight line so
angle BAE + angle CAB = 180 .................(2)

From (1) and (2) we get
angle CDB = angle BAE. ....................(3)

Because ABFE is a cyclic quadrilateral,
angle BAE + angle BFE = 180 ...............(4)

From (3) and (4) we get
angle CDB + angle BFE = 180

so CD is parallel to EF.