 hey hello friends welcome again to another session on gyms of geometry and today we are going to demonstrate a very important and very famous and very popular element in geometry which is called Simpson's line now in the previous few sessions we saw what a Pidel triangle is if you remember a Pidel triangle is nothing but if you take a point inside or outside circle and drop the three altitudes or perpendicular on to the three sides for example here D is a Pidel point just in this case it's inside the triangle and the three perpendicular have been dropped from D on to ABBC and CA of triangle ABC so you can see this is one altitude ODE, DF and DG are three altitudes not altitude sorry perpendicular from point D to the three sides and EFG is called the Pidel triangle right EFG is called the Pidel triangle we saw that and we had various other properties around Pidel triangles that the third Pidel triangle to a triangle is similar to the first triangle and things like that so you can always check those previous sessions but in this case we are going to see what happens if point D is you know shifted or let's say the location of point D changes with respect to the three sides of the triangle and what type of Pidel triangles do we get so let's try and see that so here I am I will now try to move the point D so let me just put this in the middle of the screen yeah and now I'm going to move the point D guys you can see now I'm changing the point D so for various points right inside the triangle you can see the shape and sizes of Pidel triangle now in one case you'd have noticed that if I move the point D in one particular direction so here is what I'm doing so one particular direction and now after a point the area starts getting decreased area of Pidel triangle can you see now the point D has gone out of triangle ABC and the Pidel triangle now is you know the area is getting decreased and it will be interesting to note that the moment point D reaches the circum circle okay the area becomes zero isn't it area becomes zero and that means E F G are now collinear and E F G are nothing but the foot of the perpendicular dropped from D on the three sides and they are collinear in one case what is the case when point D lies on the circum circle and this particular line E F G dear friends it's called Simpsons line so let me just change the position of D now as D go out of the circum circle you see there is another Pidel triangle which gets generated so just to show you that it's not a you know function of the location of you know one particular point of location of D you can see as I'm changing the positions of D you're getting Pidel triangles with different areas but the moment I bring point D on the circle you can see you can see that the the three perpendicular foot of feet are collinear can you see that so at any point at any point of the circum circle if you take the point and drop three perpendicular you will see the three feet of the perpendicular so dropped are collinear and that particular line joining the three feet of the perpendicular is dropped from the point D and point D happens to be where on the circum circle so if you see that particular line when you join the three perpendicular feet the line joining the three feet will be called Simpsons line now we'll try to prove this geometrically why Simpsons line exist and how do we prove that you know these three feet of the perpendicular is dropped from point D lying on a circum circle of the triangle are always collinear so we'll see the proof in the next session