Now we're introducing "Limits" in Geometry!

Geometry Level 5

Let \(m,w\) and \(h\) be the lengths of the median, the angle bisector and the altitude, respectively, from the right-angled vertex \(A\) of a triangle \(ABC\) to the hypotenuse. Suppose that the side \(c\) is fixed in length, while the side \(b\) varies subject to \(a>b \geq c\). Evaluate the value of the following correct upto three places of decimals:

\[\large{\lim_{b \to c} \dfrac{m-h}{w-h}=\ ?}\]

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