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

digram
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 $EF$?

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