Constructing triangle $\triangle ABC$ given median to the side $c$ and angles $\alpha$ and $\beta$
I started with the median. Then I constructed a circle to each side of the median, such that the circle is a set of all points which are the vertices of angle $\alpha$ and $\beta$ above the given segment (the median) respectively. Now, if I only could create a line segment $AB$, such that it passes the point $C_1$ (the endpoint of the median and the middle point of side $AB$), each endpoint is on a different circle (to get the correct angles), and the line segments $AC_1$ and $C_1B$ are the same length ($C_1$ is the endpoint of a median), I would be done. Any ideas?