What is the name of the triangle centre point with 120° subtended vertices?

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In summary, the center of a triangle is a point that is equidistant from all three vertices of the triangle, also known as the circumcenter. It can be found by using different methods such as finding the intersection point of the perpendicular bisectors of the sides or angle bisectors of the angles. The center can be inside, outside, or on the triangle depending on the type of triangle. It has geometric properties that are useful in problem-solving and is also used in constructing and inscribing circles within a triangle. A triangle can have multiple centers, with some coinciding for certain types of triangles.
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Baluncore
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TL;DR Summary
There are a couple of thousand definitions for different triangle centres.
I am looking for the name of the triangle centre point from which the vertices subtend 120°.

I am concerned really with deviant equilateral triangles, thru to right angle triangles. Flat triangles, that have an internal angle greater than 120°, do not have such a point within the triangle.

The lines from that centre point to the three vertices is the minimum total line length needed to connect the vertices.
 
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Fermat point?
 
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Thank you for the name. That appears to be correct.
 

Related to What is the name of the triangle centre point with 120° subtended vertices?

1. What is the center of a triangle?

The center of a triangle is a point that is equidistant from all three vertices of the triangle. It is often referred to as the centroid.

2. How do you find the center of a triangle?

The center of a triangle can be found by finding the intersection point of the three medians of the triangle. A median is a line segment that connects a vertex to the midpoint of the opposite side.

3. What is the significance of the center of a triangle?

The center of a triangle is an important point in geometry as it is the balancing point of the triangle. It is also used in various geometric constructions and proofs.

4. Is the center of a triangle always inside the triangle?

Yes, the center of a triangle is always inside the triangle. This is because the medians of a triangle always intersect inside the triangle.

5. Can the center of a triangle be outside of the triangle?

No, the center of a triangle cannot be outside of the triangle. This is a geometric impossibility as the medians of a triangle always intersect inside the triangle.

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