Equidistantiation
Geometry
Level
3
True or False : In 2D space, there exists 4 points equidistant with one another.
True
False
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1 solution
In 2D space, there can only be at most 3 points which can be made to be equidistant with one another.
This can be verified by drawing a circle with fixed radius r on any chosen center. Along its circumference, choose the second point, and draw a circle with the same radius. From there you will have two intersection points, both equidistant from the two chosen points (with distance r ), but whose distance to the other intersection is not the same as the radius.