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Probability of the measures

Source: Brazil Undergrad MO - Galois-Noether 2018 #12

November 26, 2019
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Problem Statement

Let ABCABC be an equilateral triangle. AA point PP is chosen at random within this triangle. What is the probability that the sum of the distances from point PP to the sides of triangle ABCABC are measures of the sides of a triangle?
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