MathDB
inscribing n circles inside big circle

Source: LIMIT 2019 CBS2 P1

April 28, 2021
geometry

Problem Statement

Let n≥3n\ge3 be integer. Assume that inside a big circle, exactly nn small circles of radius rr can be drawn so that each small circle touches the big circle and also touches both its adjacent small circles. Then, the radius of big circle is <spanclass=′latex−bold′>(A)</span> rcsc⁡πn<span class='latex-bold'>(A)</span>~r\csc\frac{\pi}n <spanclass=′latex−bold′>(B)</span> rcsc⁡(1+2πn)<span class='latex-bold'>(B)</span>~r\csc\left(1+\frac{2\pi}n\right) <spanclass=′latex−bold′>(C)</span> rcsc⁡(1+π2n)<span class='latex-bold'>(C)</span>~r\csc\left(1+\frac{\pi}{2n}\right) <spanclass=′latex−bold′>(D)</span> rcsc⁡(1+πn)<span class='latex-bold'>(D)</span>~r\csc\left(1+\frac{\pi}n\right)
Back to ProblemsView on AoPS