Question 95
Touching circles $k_1(S_1, r_1)$ and $k_2(S_2, r_2)$ lie in a right-angled triangle $ABC$ with the hypotenuse $AB$ and legs $AC = 4$ and $BC = 3$ in such way, that the sides $AB$, $AC$ are tangent to $k_1$ and the sides $AB$, $BC$ are tangent to $k_2$. Find radii $r_1$ and $r_2$, if $4r_1 = 9r_2$. (Pavel Novotný)
