Constructing triangle $\triangle ABC$ given median $AM$ and angles $\angle BAM, \angle CAM$
I start with the median $AM$. Since $\angle BAM, \angle CAM$ are known I can construct them. So I have point $A$, line segment $AM$ and $2$ rays starting from A where $\angle BAM, \angle CAM$ are those from the hypothesis. If only I could find a way to construct a line where $BM = MC$ I would be done. I can't figure out how to do that.