How to find Fermat Point in Triangle?
The Fermat point of a triangle with the largest angle at most 120° is simply its first isogonic center, which is constructed as follows:
Step 1: First, we need a triangle for finding a Fermat point. So, Draw a triangle with vertices A, B, and C.
Step 2: Then, draw an equilateral triangle on side AB of side length equal to side AB. And named it Triangle ABD.
Step 3: Similarly, let’s draw equilateral triangle’s on left sides AC and BC of their respective side lengths, and named them triangle BAE and triangle BCF.
Step 4: Now, Draw line DB.
Step 5: Similarly, draw a line between EC and FA.
Step 6: The point where these 3 lines meet is known as Fermat Line.
Note: There are different ways to find Fermat Point, but this one is popular one.
Fermat Point
Fermat Point is the point that Pierre de Fermat, the 17th-century French mathematician, posed as a challenge to his compatriot Evangelista Torricelli to geometrically determine, is named in Fermat’s honour as the solution that would minimize the total combined distance from each vertex of a triangular figure to any single internal locus. Torricelli solved the problem, therefore other than Fermat Point, it is also known as the Fermat Point or the Torricelli Point or Fermat Torricelli Point.
Although various methods exist to locate the Fermat point, connecting the vertices of the original triangle to those of the equilateral triangles constructed on each of its sides furnishes a straightforward technique. The intersection of these segments is the Fermat point.
The Fermat point gives a solution to the geometric median and Steiner tree problems for three points.
Table of Content
- What is Fermat Point or Torricelli Point?
- Fermat Point Definition
- How to find Fermat Point in Triangle?
- Different Cases of Fermat Point
- Case 1: Triangle has an Angle ≥ 120o
- Case 2: Triangle has no Angle ≥ 120o
- Properties of Fermat Point
- Important Point about Fermat Point
- Applications of Fermat Point
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