In triangle $ABC,$ $\angle C = 90^\circ.$ A semicircle is constructed along side $\overline{AC}$ that is tangent to $\overline{BC}$ and $\overline{AB}.$ If the radius of the semicircle is equal to $\frac{BC}{4},$ then find $\frac{AC}{BC}.$

In triangle ABC angle C 90circ A semicircle is constructed along side overlineAC that is tangent to overlineBC and overlineAB If the radius of the semicircle is class=