## 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.

### Submit your solution

Please do send in your solution to this problem to weeklymaths@kcl.ac.uk You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide you with feedback on your solution.