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MathNet 2006 — Part 04 Question 103

Math Olympiad Vault · MathNet 2006 — Part 04

Question 103

Farmer Martin produced 3 identical bales of hay while baling hay. The cross section of each hay bale is a circle with radius $r$. He placed the hay bales in a pyramid so that they were touching each other, and strung a rope over them, which he attached to the ground at both ends. The upper part of the rope is stretched around the circumference of the upper hay bale, and the side parts of the rope are straight and touch the lower two hay bales (see picture). Express the length of the rope with radius $r$.

Question illustration