Question 1
Circles $(K_1, r_1)$ and $(K_2, r_2)$ are tangent and also they are tangent to the sides of the rectangle $AB\Gamma\Delta$, with $AB = a$ and $B\Gamma = b$.
(i) Express the sides $a$ and $b$ with respect to the radius $r_1$ and $r_2$.
(ii) If the common internal tangent of the two circles passes through $\Delta$ compute the ratio $\frac{r_1}{r_2}$ and find the length of $\Delta K$.
(i) Express the sides $a$ and $b$ with respect to the radius $r_1$ and $r_2$.
(ii) If the common internal tangent of the two circles passes through $\Delta$ compute the ratio $\frac{r_1}{r_2}$ and find the length of $\Delta K$.