Locus of a point which is equidistant from two fixed points
On the screen, let us first see the two points A and B. A line segment AB is drawn in black color. A right angled perpendicular bisector of this line segment is also drawn, it is in red color and point C is at its foot. Now we take a free point D on the plane and line segments AD and BD are drawn. Now move the points A, B and D and observe how the lengths of AC, BC, AD and BD get changed.
1. What do we observe when AD=DB? 2. What do we observe when point D lies on the red perpendicular bisector?