Geometry · Tangent lines · Circles · Arc length · Equilateral triangle
Farmer Martin has made \(3\) identical bales of hay. The cross-section of each bale is a circle of radius \(r\). He stacks the bales into a pyramid, each bale touching the other two, and stretches a rope over them, pinning both ends of the rope into the ground. The upper part of the rope lies taut along the circumference of the top bale, while the two side parts are straight and touch the two lower bales, as in the figure. Express the length of the rope in terms of \(r\).
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), odbirno (qualifying) round 2022, 1. letnik, category A, problem 2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source