Lemoine's problem

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Lemoine's problem is a straightedge-and-compass geometry puzzle proposed by French mathematician Émile Lemoine in 1868. It appeared as Question 864 in the 1868 issue of Nouvelles Annales de Mathématiques. The best-known part of the story is Ludwig Kiepert's 1869 solution, which described a hyperbola now called the Kiepert hyperbola. Kiepert proved his construction with a few lemmas. Several other mathematicians also submitted solutions around 1868–69, including Williere, Brocard, Claverie, Joffre, Racine, Augier, Niebylowski, and L. Henri Lorrez, but Kiepert's solution was the most complete.