2007 Cyprus MO/Lyceum/Problem 21

Problem

In the figure, three equal cycles of diameter $20\,\mathrm{ cm}$ represent pulleys, that are connected with a strap. If the distances between any two pulley center points are $AB=3\,\mathrm{m}$ , $AC=4\,\mathrm{m}$ and $BC=5\,\mathrm{m}$ , then the length of the strap is

The lengths of the straight parts of the strap are $3\,\mathrm{m}$ , $4\,\mathrm{m}$ , and $5\,\mathrm{m}$ . Their sum is $12\,\mathrm{m}$ . The curved parts of the band add up to a full circumference of one of the circles, so their sum is $20\pi\,\mathrm{m}$ . The total length of the strap is $(12+20\pi)\,\mathrm{m}\Longrightarrow\mathrm{A}$ .