Given any triangle ABC:
Construct equilateral triangles
ABD, BCE, and CAF :
Construct segments DC, EA,
and FB. The intersection of DC, EA, and FB creates point P :
Final Product produces
AP+BP+CP= the minimum sum of distances between the three vertices:
Why does this work? Investigate A
Proof!
There are several ways to prove this problem. In researching,
I found that one web site does an excellent job of providing alternate
examples of proofs and investigations called
The
Fermat Point and Generalizations!
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