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Triangles from products of sides with cevians

By Z. Čerin


We consider the problem of determining for which central points X of the triangle ABC the products of lengths of sides and cevians of X will be sides of a triangle. We shall prove that twenty-seven out of hundred and one central points from the Kimberling\u27s list have this property. The algebraic method of proof for this result is also used to obtain some new examples of three segments that are sides of a triangle and are built from elements of a given triangle

Topics: triangle; cevian; triangular; central point; isogonal conjugate
Publisher: Department of Mathematics, University of Osijek
Year: 1998
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