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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.

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