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
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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