Challenge 279: Proximity Probability
Freddy the fly lands in a large triangle with vertices A, B and C which has been marked out on the floor of the school hall by an enthusiastic teacher.
The side lengths of the triangle are AB = 5m, BC = 12m and CA = 13m.
What is the probability that Freddy lands on a spot which is closer to A than to C, but is also closer to B than A?
Explain your method clearly and give your answer as an exact value.