Question 33
$C_1$, $C_2$, $C_3$ are circles, none of which lie inside either of the others. $C_1$ and $C_2$ touch at $Z$, $C_2$ and $C_3$ touch at $X$, and $C_3$ and $C_1$ touch at $Y$. Prove that if the radius of each circle is increased by a factor $2 / \sqrt{3}$ without moving their centers, then the enlarged circles cover the triangle $XYZ$.