Question 18
Let $C_1$ and $C_2$ be circles defined by $$
(x - 10)^2 + y^2 = 36
$$ and $$
(x + 15)^2 + y^2 = 81,
$$ respectively. What is the length of the shortest line segment $\overline{PQ}$ that is tangent to $C_1$ at $P$ and to $C_2$ at $Q?$
(x - 10)^2 + y^2 = 36
$$ and $$
(x + 15)^2 + y^2 = 81,
$$ respectively. What is the length of the shortest line segment $\overline{PQ}$ that is tangent to $C_1$ at $P$ and to $C_2$ at $Q?$