Triangle Formed By Intercepts

Geometry Level 4

In \(\triangle ABC\) \( AB = 10\) and \(AC = 15\). \(AE\) is the median from \(A\) and \(AD\) is the internal bisector of \(\angle BAC\). The point \(P\) is on \(AC\) such that \(AP = 6\). \(BP\) intersects \(AD\) at \(N\) and \(AE\) at \(M\). What is the value of

\(\dfrac{[ABC]}{[ANM]}\) ?

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