Found problems: 1
2018 BMT Spring, 9
Circles $A$, $B$, and $C$ are externally tangent circles. Line $PQ$ is drawn such that $PQ$ is tangent to $A$ at $P$, tangent to $B$ at $Q$, and does not intersect with $C$. Circle $D$ is drawn such that it passes through the centers of $A$, $B$, and $C$. Let $R$ be the point on $D$ furthest from $PQ$. If $A$, $B$, and $C$ have radii $3$, $2$, and $1$, respectively, the area of triangle $PQR$ can be expressed in the form of $a+b\sqrt{c}$, where $a$, $b$, and $c$ are integers with $c$ not divisible by any prime square. What is $a + b + c$?