High Quality Content by WIKIPEDIA articles! In Euclidean geometry, Carnot's theorem, named after Lazare Carnot (1753–1823), is as follows. Let ABC be an arbitrary triangle. Here the sign of the distances is taken negative if and only if the line segment DX (X = F, G, H) lies completely outside the triangle. In the picture DF is negative and both DG and DH are positive. Carnot's theorem is used in a proof of the Japanese theorem for concyclic polygons.

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