The lost daughters of Gergonne


Abstract. Given a triangle center we can draw line segments from each vertex through the triangle center to the opposite side, this splits the triangle into six smaller triangles called daughters. Consider the following problem: Given a triangle S and a rule for finding a center find a triangle T, if possible, so that one of the daughters of T, when using the rule is S. We look at this problem for the incenter, median and Gergonne point. 1

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