You can't bash it out

Geometry Level 3

\(P\) is a point on the base \(BC\) of a \(\triangle(ABC)\) and \(r_{1},r_{2},r_{3}\) be the in-radii of the triangles \(ABC,ACP,ABP\) respectively , \(h_{a}\) is the length of altitude from \(A\) to \(BC\). Find \(h_{a}\) given that \(r_{1}=5,r_{2}=3,r_{3}=4\).

Bonus: Try to generalisze it.

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