KöMaL 2015 B4737

$D$ is the foot of the altitude drawn to the hypotenuse $AB$ of a right-angled triangle $ABC$ . The angles bisectors of $\angle ACD$ and $\angle BCD$ intersect hypotenuse $AB$ at $E$ and $F$ , respectively. Determine the ratio of the inradius of triangle $ABC$ to the circmradius of triangle $CEF$ .