jmc

By the angle bisector theorem, $AC/CD=AB/BD=105/42=5/2$. Let $AC=5x$ and $CD=2x$.



Then by Pythagoras, $(2x+42{)}^2+105^2=(5x{)}^2$. This simplifies to $21x^2-168x-12789=0$, which factors as $21(x-29)(x+21)=0$, so $x=29$. Therefore, $AC=5x=\boxed{145}$.