Join AB. Label Ð CAB as a, then find angles EAB, CDB and EFB all in terms of a. You will need to use the fact that the opposite angles of a cyclic quadrilateral add up to 180 degrees.

If you are not sure why then see the article on Cyclic Quadrilaterals.

What did you notice about the line segments CD and EF as C and D move around thecircle ?

By considering two of these angles can you now prove what your eyes told you about CD and EF?