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Two points $D$ and $E$ are taken inside the triangle $ABC$ such as$\angle{ABD}=\angle{EBC}$ From the point $D$ two perpendicular lines $DF$ and $DG$ are drawn to $AB$ and $BC$ respectively . From the point E two perpendicular lines $EH$ and $EI$ are drawn to $AB$ and $BC$ respectively .$ DF=8,DG=9,EI=17, EH=$?

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