Lisa, bree, and caleb are meeting at an amusement park. they each enter at a different gate. on this diagram of the park, explain how the friends could calculate the point that is equidistant from all three gates.

Denote the points wherein Lisa, Bree, and Caleb are by L, B and C.
Suppose that the three points are not linear. Otherwise the equidistant 
point is on the line that goes through L, B and C. 
We can think different aspect of the equidistance point E. 
Since EL=EB=EC, then E is the centre of the circle that passes through 
the points LBC.
Furthermore, if we draw the three circles with centers L, B and C, then 
those circle will intersect in only one point P if 
P is the equidistance point E. 
So there is two geometric constructions with circles. 

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