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Minimal distance from a point inside a triangle to vertices. (Posted on 2010-05-22) Difficulty: 4 of 5
Given a triangle whose angles are less than 120 degrees.

Find the point inside the triangle such that the sum of distances to all three vertices is minimum.

No Solution Yet Submitted by Vee-Liem Veefessional    
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Solution Fermat point Comment 2 of 2 |
 

In order to locate the Fermat point of a triangle with largest angle at most 120: <br>

  1. Construct three*  regular triangles out of the three sides of the given triangle.
  2. For each new vertex of the regular triangle
     draw a  line from it to the opposite triangle's vertex.
  3. These three lines intersect at the Fermat point.

 

When a triangle has an angle greater than 120 the Fermat point is sited at the obtuse angled vertex. 

 Pasted from <http://en.wikipedia.org/wiki/Fermat_point>

 

*Clearly, two is enough.
 


  Posted by Ady TZIDON on 2010-05-22 20:27:36
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