Carnot’s and Haruki’s theorems. (I teoremi di Carnot e di Haruki.) (Italian. English summary)

Archimede 62, No. 1, 16-19 (2010).

Summary: In this paper we present some similarities between Hiroshi Haruki’s and Carnot’s theorems. They both refer to the ratios of lengths of line segments that recall Ceva’s theorem. Haruki’s theorem refers to three circles, each intersecting the other two in two points. Carnot’s theorem deals with the segments that are formed when a circle intersects a triangle in six points. The proofs are based on similarity.