explain how the friends can calculate the point that is equadistant from all three gates if they enter 3 diffrent gates

Question

there are 3 gates and 3 friends

Answer 1

There is a line consisting of points that are equidistant from points A and B. It is the perpendicular bisector of segment AB .It connects two points formed by arcs which cross (see figure). The distance between points A and B is a convenient radius for these arcs.

Likewise, there is a line consisting of points that are equidistant from points B and C (see figure). It contains two other points where other arcs cross (see figure again).

These two lines intersect at one point that is equidistant from points A, B, and C. Note that this point is also on the line formed by the perpendicular bisector of the segment CA,

This special point (equidistant from every point on the circle) is called the Center, Its distance from A, B, and C is called the Radius.