First Fermat Point and Isogonic Center of a Triangle

This Demonstration plots the first Fermat point

FFP

(red) and first isogonic center

FIC

(yellow) of a triangle

T

. You can drag the triangle vertices. When

FFP

and

FIC

are both inside the triangle, they coincide.

Let

F(P,T)

be the sum of the distances from a point

P

to the three vertices of

T

. Then

FFP

minimizes

F

. The contours show the level lines of

F

.