IMO 1961 Problem 5

Construct a triangle $ABC$ if $AC=b$ , $AB=c$ and $\angle AMB=w$ , where $M$ is the midpoint of the segment $BC$ and $w<90$ . Prove that a solution exists if and only if $$b \tan{\dfrac{w}{2}} \leq c <b$$ In what case does the equality hold?