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For a spherical convex body $K\\subset \\mathbb S^n$ of constant width $w\\in(0,\\pi)$, its relative effective radius is \\[\n  \\left(\\frac{\\mu_n(K)}{\\mu_n(\\mathbb B^n(w/2))}\\right)^{1/n}, \\] where $\\mu_n$ is the spherical $n$-measure and $\\mathbb B^n(w/2)$ is a geodesic ball of radius $w/2$. 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