isogonic centers | isogonic points | Torricelli point

In a given triangle Δ A B C with all angles less than 120° (2π/3, the first Fermat point X or F_1 (sometimes simply called "the Fermat point, " Torricelli point, or first isogonic center) is the point X which minimizes the sum of distances from A, B, and C, left bracketing bar A X right bracketing bar + left bracketing bar B X right bracketing bar + left bracketing bar C X right bracketing bar . This problem is called Fermat's problem or Steiner's segment problem and was proposed by Fermat to Torricelli. Torricelli's solution was published by his pupil Viviani in 1659.

Brocard angle | equilateral triangle | Fermat axis | first Fermat point | isodynamic points | isogonal conjugate | Lester circle | second Fermat point | Steiner's segment problem