Question: How many lines can be drawn in a 2D plane such that they are equidistant from 3 non-collinear points ?

Solution: The three non-collinear points form a triangle. There will be 3 lines which are equidistant from all the three points.
Draw altitudes from each point to the line joining the other two points.We get 3 altitudes.Now draw a line passing through the mid point of the altitude line and parallel to line onto which the altitude is drawn.This line is equidistant from all the 3 points.Thus we get 3 lines.