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'Defined Distances' printed from http://nrich.maths.org/
We plot $J$ and $K$ $13$ apart. There are a number of options for
where to add $L$ and $M$, but working systematically we find that
only one option is consistent with $MJ$ being $12$. The final
layout looks like
The distance between the points furthest apart is
This problem is taken from the UKMT Mathematical Challenges.