Geometry · Circle arc length · Semicircles · Perimeter · Invariance
Five semicircles, all of different sizes, stand side by side on one straight segment: each semicircle has its diameter on the segment, consecutive semicircles touch, and the five diameters together fill the whole segment, whose length is \(10\). All five arcs are drawn on the same side of the segment, as in the figure. What is the perimeter of the shape formed in this way?
- A \(5\pi\)
- B \(10\pi\)
- C \(10 + 5\pi\)
- D \(10 + 10\pi\)
- E The perimeter depends on the diameters of the semicircles.
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2025, 1. letnik, category A, problem A1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source