Given the "peaks" of three equilateral triangles placed on the sides of a triangle 
, construct 
. The problem was proposed by Lemoine (1868) and solved for
the general case of isosceles triangles by
Kiepert (1869) using the Kiepert hyperbola.
Lemoine's Problem
See also
Equilateral Triangle, Isosceles Triangle, Kiepert Hyperbola, Outer Napoleon TriangleExplore with Wolfram|Alpha
References
Eddy, R. H. and Fritsch, R. "The Conics of Ludwig Kiepert: A Comprehensive Lesson in the Geometry of the Triangle." Math. Mag. 67, 188-205, 1994.Kiepert, L. "Solution de question 864." Nouv. Ann. Math. 8, 40-42, 1869.Lemoine, É. "Question 864." Nouv. Ann. Math. 7, 191, 1868.Referenced on Wolfram|Alpha
Lemoine's ProblemCite this as:
Weisstein, Eric W. "Lemoine's Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LemoinesProblem.html