Question 49
Two circles $k_1(S_1, r_1)$ and $k_2(S_2, r_2)$ are externally tangent and both lie in a square $ABCD$ with side length $a$ so that $k_1$ touches the sides $AD$ and $CD$, while $k_2$ touches the sides $BC$ and $CD$. Prove that the area of at least one of the triangles $AS_1S_2$, $BS_1S_2$ is no more than $\frac{3}{16}a^2$. (Tomáš Jurík)