Enigma 261: Point in square
26 February 2015
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From New Scientist #1408, 3rd May 1984 [link]
It took some hours for the ZX Spectrum I received for Christmas to produce this pretty specimen of an integral-sided square, with a point P lying inside it at integral distances from three of the square’s corners.
If you use a computer, it will probably take you just as long to find another such specimen with smaller square-side. But without a computer, it is possible to find a solution in a fraction of the time. P must be inside the square, not outside or on the edge.
What is the length of the side of the smaller square and what are the distances PA, PB, PC?