7. As shown in the figure, ABCD is a cyclic quadrilateral, point $C$ is the midpoint of $\overparen{B D}$, the tangent $C E$ intersects the extension of $A D$ at $E$, and $A C$ intersects $B D$ at $F$. Then the number of pairs of line segments whose ratio is equal to $\frac{A E}{C E}$ is ( ).
(A)5
(B) 6
(C) 7
(D) 8
7. (C).

As shown in the figure, it is easy to know that
$$
\frac{A E}{C E}=\frac{C E}{D E}=\frac{A D}{F D}=\frac{A B}{B F}=\frac{B C}{C F}=\frac{D C}{C F}=\frac{A C}{D C}=\frac{A C}{B C} .
$$