This note studies a cubic curve in a triangle that meets the Menelaus-Ceva condition, indicating its properties.
This note aims to study the cubic curve naturally associated to a triple of strictly positive numbers satisfying the Menelaus-Ceva condition. Restricting to a fixed triangle Δ we discuss several main points and the Lemoine line of Δ in this unified framework and we point out the cases when the cubic curve is an elliptic one.
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Mircea Crasmareanu (2026) studied this question.
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