# 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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