Smallest Equilateral Triangle with Internal Point at Integer Distances from Vertices

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

• 1990: Hugh ApSimon: More Mathematical Byways

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $112$