Ononot — In \triangle ABC, the side lengths are a=7, b=24, c=25. A li

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Euclidean 2Dhard

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In $\triangle ABC$ , the side lengths are $a=7, b=24, c=25$ . A line segment $DE$ is drawn parallel to $AB$ with $D$ on $AC$ and $E$ on $BC$ such that the area of $\triangle CDE$ is $\frac{1}{16}$ the area of $\triangle ABC$ . What is the length of $DE$ ?