Mark 3 points not in a straight line. By construction, find the..

Find the point which is equidistant from these three points?

The point you need is the circumcenter of the triangle having the three points as vertices. To construct the circumcenter, construct the perpendicular bisectors of two sides of the triangle. They intersect at the required point.

http://whistleralley.com/construction/c1…

Let's choose the points:
(0, 0), (1, 1) and (2, 4) which are all derived from the graph of y = x^2
If it's equidistant, then there exists a point (x, y) such that:
sqrt(x^2 + y^2) = sqrt((x - 1)^2 + (y - 1)^2) = sqrt((x - 2)^2 + (y - 4)^2)
x = -3 and y = 4
(-3, 4) is the point.

3 points are vertices of equilateral triangle....
the required point is the point where angular bisector meet
good luck

So what's your question? We can't do constructions here.

Mark the points like you're told, get three equal sticks, put one on each point, and see where they all meet.

Ta-Daaa!