Triangle given the A-median m, the A-bisector d, and the product bc of the sides

1) Draw a segment AD' with length 2bc/d.
2) The circle with center A and radius d cuts AD' at D.
3) The circle with diameter DD' cuts at M the circle with center A and radius m.
4) The perpendicular bisector of AD' cuts D'M at O.
5) The circle with center O and going through A cuts MD at B and c, and ABC is the requested triangle.