Question 165
We are given triangle $ABC$, with $AB = 9$, $AC = 10$, and $BC = 12$, and a point $D$ on $BC$. $B$ and $C$ are reflected in $AD$ to $B'$ and $C'$, respectively. Suppose that lines $BC'$ and $B'C$ never meet (i.e., are parallel and distinct). Find $BD$.