Triangle

Geometry Level 3

Let \(ABC\) be a triangle and \(AD\) perpendicular on \(BC\), \(D\) is situated on \(BC\) .Let \(M\) be the midpoint of \( AD\) and \(N\) the midpoint of \(AB\). Let \(T\) be the intersection of BM with CN and S the intersection of AD with CN. If BM is perpendicular on CN and NT=2 and SC=9,find ST and the area of triangle ABC.

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