A geometry problem by Walid Mustafa

Geometry Level 4

\(In\quad \triangle ABC\quad in\quad the\quad adjoining\quad figure,\quad AD\quad and\quad AE\quad\) \(trisect\quad \angle BAC.\quad The\quad lengths\quad of\quad BD,\quad DE\quad and\quad EC\quad are\) \( 2,\quad 3,\quad and\quad 6,\quad respectively.\quad\) \(Find\quad the\quad length\quad of\quad the\quad shortest\quad side\quad of\quad \triangle ABC.\)

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