Smallest Equilateral Triangle with Internal Point at Integer Distances from Vertices
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Theorem
The smallest equilateral triangle with sides of integer length which contains a point which is an integer distance from each vertex has a side length $112$:
There exists a point inside it which is $57$, $65$ and $73$ away from the three vertices.
Proof
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Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $112$