Question 82
There are two touching circles, $k_1(S_1, r_1)$ and $k_2(S_2, r_2)$ in a rectangle $ABCD$ with $|AB| = 9$, $|BC| = 8$. Moreover, $k_1$ touches $AD$ and $CD$, while $k_2$ touches $AB$ and $BC$.
a) Prove $r_1 + r_2 = 5$.
b) What is the least and what is the greatest possible area of $AS_1S_2$?
a) Prove $r_1 + r_2 = 5$.
b) What is the least and what is the greatest possible area of $AS_1S_2$?