HMMT 2008 S10

Let $a, b, c$ denote the side lengths of $B C, C A, A B$ . Find the lengths of $A E, B F, C D$ in terms of $a, b, c$ .

Dataset text NuminaMath olympiads. Quoted with source.

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\begin{aligned} & A E=\frac{b+c-a}{2}, \ & B F=\frac{a+c-b}{2}, \ & C D=\frac{a+b-c}{2} \end{aligned}

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