# what is the fermat point of a triangle and its construction steps with proof

Aman Bansal
592 Points
12 years ago

Dear Vedant,

In order to locate the Fermat point of a triangle with largest angle at most 120°:
1. Construct two regular triangles out of any the three sides of the given triangle.
2. For each new vertex of the regular triangle, draw a line from it to the opposite triangles vertex.
3. The two lines intersect at the Fermat point.

An alternate method is the following:
1. On any two of the three sides, construct two isosceles triangles, with base the side in question, 30-degree angles at the base, and vertices laying outside the original triangle.
2. Draw two circles, each with center on the vertex of the just constructed isosceles triangles and radius the identical side of the isosceles triangles.
3. The intersection inside the original triangle between the two circles is the Fermat point.

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Thanks

Aman Bansal