Think Twice | The Fermat Point of a Triangle | Geometric construction + Proof | @ThinkTwiceLtu | Uploaded February 2020 | Updated October 2024, 2 days ago.
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Summary:

The Fermat point of a triangle ABC is a point P such that the sum of distances PA+PB+PC is a minimum.

To find the Fermat point of a triangle ABC:
1. Construct equilateral triangles on each side of ABC
2. Connect vertices A,B and C to the opposite and outermost vertex of equilateral triangle.
3. The point at which the three lines intersect is a Fermat point of triangle ABC.

In the case where one of the angles of triangle ABC is greater than 120 degrees the Fermat point will be located at the obtuse-angled vertex of ABC.

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