A Pre-RMO question! -27

Geometry Level 2

Let AH,AD\overline{AH},\overline{AD} and AM\overline{AM} be an altitude, an angle bisector, and a median of ABC\triangle ABC. If AB=14\overline{AB}=14, AC=10\overline{AC}=10, BC=18\overline{BC}=18, and the area of ADM\triangle ADM is 7k4\dfrac{7\sqrt{k}}{4}, find value of kk.

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