2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75831S. L. Tabachnikov's conjecture is proved: for any closed curve $Γ$ lying inside convex closed curve $Γ_1$ the mean absolute curvature $T(Γ)$ exceeds $T(Γ_1)$ if $Γ\ne kΓ_1$. An inequality $T(Γ)\ge T(Γ_1)$ is proved for curves in a hemisphere.Metric Geometry52A38, Secondary: 52A40text