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In a triangle $A B C$ assume $A B=A C$, and let $D$ and $E$ be points on the extension of segment $B A$ beyond $A$ and on the segment $B C$, respectively, such that the lines $C D$ and $A E$ are parallel. Prove $C D \geq \frac{4 h}{B C} C E$, where $h$ is the height from $A$ in triangle $A B C$. When does equality hold?
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