Cities $A,B,C,D$ are positioned in such a way that $A$ is closer to $C$ than to $D$, and $B$ is closer to $C$ than to $D$. Prove that every point on the straight road from $A$ to $B$ is closer to $C$ than to $D$.
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Tags: combinatorics
Cities $A,B,C,D$ are positioned in such a way that $A$ is closer to $C$ than to $D$, and $B$ is closer to $C$ than to $D$. Prove that every point on the straight road from $A$ to $B$ is closer to $C$ than to $D$.