Too many lines

Geometry Level pending

In a triangle \(ABC \), \(AD\) is a median. \(E\) is the midpoint of \(BD\). Segment \(CF\) is drawn through \(P\), the midpoint of \(AD\), with \(F\) on \(AB\). \(DG\) is drawn parallel to \(CF\) with \(G\) on \(AB\). \(AE\) cuts \(DG\) at \(H\). Find the ratio of the area of triangle \(ADH\) to the area of triangle \(ABC\). Give answer in decimals.

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