ISL 1994 G1

$C$ and $D$ are points on a semicircle. The tangent at $C$ meets the extended diameter of the semicircle at $B$ , and the tangent at $D$ meets it at $A$ , so that $A$ and $B$ are on opposite sides of the center. The lines $AC$ and $BD$ meet at $E$ . $F$ is the foot of the perpendicular from $E$ to $AB$ . Show that $EF$ bisects angle $CFD$