KöMaL 2017 B4861

Let $r$ and $R$, respectively, denote the radii of the inscribed and circumscribed circles of a right-angled triangle $ABC$. Let $CD$ be the altitude drawn to the hypotenuse $AB$. Draw the square $CEFG$ of side length $CD$ that has vertex $E$ on side $AC$ and vertex $G$ on side $BC$. Let $T$ and $t$, respectively, denote the parts of the area of the square $CEFG$ which lie inside and outside the triangle $ABC$. Prove that $\frac{t}{T}=\frac{r}{2R}.$