Let $w$ be a circle of diameter $5$. Four lines were drawn dividing $w$ into $5$ "strips", each of width $1$. The strips were colored orange and purple alternatingly, as depicted. Which area is larger: the orange or the purple?
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Source: 2022 Israel National Olympiad P3
Tags: geometry, geometric inequality
Let $w$ be a circle of diameter $5$. Four lines were drawn dividing $w$ into $5$ "strips", each of width $1$. The strips were colored orange and purple alternatingly, as depicted. Which area is larger: the orange or the purple?