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3A_{2015} + B_{2015}> 4A_{4030}, area regular n-gons inequality

Source: 2016 Peru Cono Sur TST P2

February 26, 2020
geometrygeometric inequalityinequalitiesareaspolygon

Problem Statement

Let ω\omega be a circle. For each nn, let AnA_n be the area of a regular nn-sided polygon circumscribed to ω\omega and BnB_n the area of a regular nn-sided polygon inscribed in ω\omega . Try that 3A2015+B2015>4A40303A_{2015} + B_{2015}> 4A_{4030}
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