The Mathsbombe Competition

2023 edition. From the people behind the Alan Turing Cryptography Competition.
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Problem 3

Let P be a randomly selected point inside an equilateral triangle, and let d1,d2 and d3 be the distances between P and each of the three sides of the triangle. What is the probability that there exists a triangle with sides of length d1,d2,d3? Give your answer as a decimal rounded to two decimal places.

Mathsbombe Competition 2023 is organised by the The Department of Mathematics at The University of Manchester.
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