18. 8 (IMO 42 Preliminary) Let $\triangle A B C$ be an acute triangle, and construct isosceles $\triangle D A C$, $\triangle E A B$, and $\triangle F B C$ outside $\triangle A B C$ such that $D A=D C$, $E A=E B$, $F B=F C$, $\angle A D C=2 \angle B A C$, $\angle B E A=2 \angle A B C$, and $\angle C F B=2 \angle A C B$. Let $D^{\prime}$ be the intersection of line $D B$ and $E F$, $E^{\prime}$ be the intersection of $E C$ and $D F$, and $F^{\prime}$ be the intersection of $F A$ and $D E$. Find the value of $\frac{D B}{D D^{\prime}}+\frac{E C}{E E^{\prime}}+\frac{F A}{F F^{\prime}}$.
18. 8 It can be proven using the given conditions that: $\angle A D C, \angle B E A, \angle C F B, \angle D A E, \angle E B F, \angle F C D$ are all less than $\pi$.
$D A E B F C$ is a convex hexagon, and $\angle A D C + \angle B E A + \angle C F B = 2 \pi$. Construct three circles with centers at $D, E, F$ and radii $D A, E B, F C$ respectively. Given that $\angle A D C + \angle B E A + \angle C F B = 2 \pi$, these three circles intersect at a common point (the intersection of any two circles must lie on the third circle), let this point be $O$.

At this point, $O$ is symmetric to $C$ with respect to $D F$; $O$ is symmetric to $A$ with respect to $D E$; $O$ is symmetric to $B$ with respect to $E F$. Therefore, we have $D B: D D^{\prime} = 1 + D^{\prime} B: D D^{\prime} = \cdots = 1 + (S_{E F O}: S_{D E F})$; similarly, we have two other equations $\cdots \cdots$, adding them up gives a result of 4.