jmc

The Angle Bisector Theorem tells us that $$\frac{AX}{AC}=\frac{BX}{BC}$$ so cross multiplying and substituting tells us $$56AX=28BX$$ or $BX=2AX$.

We want to find $AX$, so we write $$50=AB=AX+XB=AX+2AX=3AX.$$ Solving gives us $AX=\boxed{\frac{50}{3}}$.