 Hello and welcome to the session. In this session we discuss the following question which says, what is the locus of a point equidistant from three collinear points A, B and C? Before we move on to the solution, let's discuss the locus theorem. To be used in this question, the theorem is the locus of a point equidistant from two fixed points is the right bisector of the straight line joining the fixed points. This is the key idea that we use for this question. Let's proceed with the solution now. Consider the three points A, B and C. Here we have A, B and C are three to find the locus of a point equidistant from the three collinear points A, B and C. From the key idea, we know that the locus of a point equidistant from the two fixed points is the right bisector of the straight line joining the fixed points. The locus of a point equidistant from the two fixed points A and B would be the right bisector of A, B. Now, this line M1 is the right bisector of A, B. Now, we can say that locus of the point from B is M1, which is the right bisector A, B. Now again, locus of the point equidistant from two fixed points B and C would be the right bisector of the line joining B and C. So now, as you can see, this line M2 is the right bisector B, C. Therefore, locus of the point equidistant from two fixed points B and C is M2, which is the right bisector of B, C. So that we have M1 is the locus of the point equidistant from the fixed points A and B and M2 is the locus of the point equidistant from two points B and C. Now since that is the line joining the three points A, B and C or you can say AC, therefore the lines M1 and M2 are parallel to each other. That is, it means that M1 and M2 have no point. This implies that locus of a point equidistant from three collinear points A, B and C does not exist. Since we know that M1 is the locus of the point equidistant from A and B, M2 is the locus of the point equidistant from B and C and both the lines M1 and M2 are parallel and they do not have any point in common. So, locus of the point equidistant from the three collinear points A, B and C does not exist. So this completes the session. We have understood the solution of this question.