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Radon transforms on piecewise smooth curves in are rather unfamiliar and have not been so far widely investigated. In this paper we consider three types of Radon transforms defined on a pair of half-lines in the shape of a V, with a fixed axis direction. These three Radon transforms arise from recently suggested tomographic procedures. Our main result consists in obtaining their analytic inverse formulas, which may serve as mathematical foundation for new imaging systems in engineering and physics.