I want to construct one triangle $ABC$ by using edge and compass. I know that $\overline{AB}=c, \overline{AC}=b$ and the measure of the median relative to side $BC$ is $m_{a}$.
Here is what I have thought. First I constructed the triangle $XYZ$ such that $\overline{XY}=c, \overline{XZ}=c$ and $\overline{YZ}=2m_{a}.$ Let $M$ be the midpoint of $YZ$. On the half-line XM I marked the point $X'$ such that $\overline{XM}=\overline{MX'}$. Therefore the triangles $MYX$ and $MX'Z$ are similar. The triangle $XZX'$ is the triangle that I am trying to construct. But there is (at least) one error here, because I do not know if I can construt the triangle $XYZ$.
I would appreciate your help.