Abstract
A finite planar set is k-isosceles for k≥3 if every k-point subset of the set contains a point equidistant from two others. We show that an 8-set on a line is 5-isosceles if and only if its adjacent interpoint distances are equal to each other, and no 5-isosceles 9-set has 9 points on a line. We also show that the maximum 5-isosceles set with 8 points on a line contains at most 10 points.
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