Question 221496
Points  A &  B  are  10 units apart
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ALL  points  equidistant,  in  2d,,are  on  the  perpendicular  bisector of  AB
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If  points  are  6  units  from  A,,,,they  are  also  6  units  from  B
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Using  the  Pythagorean  Theorem,c^2 = a^2 +b^2,  ,,,on  the  right  triangle
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legs  5 (10/2) and x,,,and  hypotenuse  6,,,
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6^2 = 5^2 + x^2,,,,36-25 = 11 = x^2
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x= sqrt 11= +/- 3.317
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That  is,  There  is  a  point  +3.317  above  the  midpoint,  and  another  point 3.317 below  the  midpoint,  in  2 Dimension
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In  3  Dimensions,  it  can  be  visualized,  an  infinite numbers  of  points, in a  circle, 
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on  the  plane perpendicular  to the  midpoint  of  AB,  with  a  radius
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of  3.317
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