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MathNet 2020 — Math Olympiad Vault — Part 05 Question 17

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 05

Question 17

On the grid in the figure, two or more grid-intersection points are called equidistant with respect to a fixed point when their distances from that point are equal. For example, $B$ and $C$ are equidistant with respect to $A$, but $B$ and $D$ are not.

Question illustration

a) Mark on the following grid the points equidistant with $K$ with respect to $J$.

Question illustration

b) If the points need not be grid intersections, what figure is formed in the grid plane by the points equidistant with $K$ with respect to $J$?

c) If the points need not lie in the grid plane, what figure is formed by the points equidistant with $K$ with respect to $J$?