Question 3
A triangle has vertices $A(0, 0),$ $B(12, 0),$ and $C(8, 10).$ The probability that a randomly chosen point inside the triangle is closer to vertex $B$ than to either vertex $A$ or vertex $C$ can be written as $\frac{p}{q},$ where $p$ and $q$ are relatively prime positive integers. Find $p + q.$