Consider a point P inside a reference triangle Δ A B C, construct line segments A P, B P, and C P. The Ehrmann congruent squares point is the unique point P such that three equal squares can be inscribed internally on the sides of Δ A B C such that they touch the line segments in exactly two points each. The side lengths of these triangles are given by the smallest root of the cubic equation a^2/(a - L) + b^2/(b - L) + c^2/(c - L) = (2Δ)/L, and the center function is α_1144 = a/(a - L), which is Kimberling center X_1144.
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