geometry

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Let the incircle of triangle $ABC$ be tangent to sides $\overline{BC}$, $\overline{AC}$, and $\overline{AB}$ at $D$, $E$, and $F$, respectively. Prove that triangle $DEF$ is acute.

I have tried proving that triangle DEF's angles were les than the opposite angles in triangle ABC, but that wasn't really complete. Can anyone help?

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