Ononot — In a triangle ABC, let I be the incenter. A line parallel to

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Euclidean 2Dhard

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In a triangle $ABC$ , let $I$ be the incenter. A line parallel to $BC$ passes through $I$ and intersects $AB$ at $D$ and $AC$ at $E$ . If $AB=12, AC=15,$ and $BC=18$ , what is the perimeter of triangle $ADE$ ?