 So I haven't made a video in a while I probably won't I might be making C programming tutorials, but I'm not sure if I know enough to be qualified on making tutorials per se But anyways, you might have seen my conic sections video on how to find Conic based on based on some points So before we did that unit in my pre-calculus class As a as an exercise for myself. I tried to see how you could find a circle with only three points and The argument it's actually pretty seem pretty pretty simple Don't mind this monstrosity here When you do it like manually with you know like a pen and paper and you don't have to account for every point Then it's pretty easy So as you can see I whipped up something really quick in Desmos, so so yeah, let me just start Okay, so let's say you have a point three points point a Point B and And point C so by definition a Circle that would touch all of these points It would mean that it would have to be equally distant from every single point So the distance from point A to to the center and the distance from point B to the center and for point C as well Would have to be the same But the first start let's just let's just find all the points that Would make that would have us all the points of the center of the circle that would touch a and B So really we only need to find The center of the circle and we could just find the radius by just Figuring out the difference between the point and any single other point, but that doesn't right now That doesn't really matter Let's just focus on finding a center So the obvious first thing would be to get the midpoint between a and B because those this point is equally distant from a and from B and Just through normal observation you can see that if you make a line like this All the points in that line would be equally distant from a and B Now I Don't really have a proof for this It just sort of seems obvious that this would always make a nice and I saw Salis triangle so But the definition of this line the slope of this line would be the inverse slope of the line that a and B make So so yeah The way the way you would find this is Let's say a and B make points a x are defined by a x and a y and B is B x and B y So if you want to find Ah, I just realized how tedious this is sort of this is gonna be to write in variable with variables But basically, yeah, you just do You just do rise over run a y minus B y over a x minus B x That would give you that if you want the inverse you would take Well, you would take the inverse So it would be let's say I'm as a slope you would take and raise to the power of negative one and then subtract And let's just say that's Let's just say that's the new M or S for slope Then you just do x minus where this midpoint is Let's say a MX this is this is getting complicated plus the y value so my Okay, that's sort of going on a side thing The important thing is that you just have to make a line That's inverse the slope that a and B makes that goes through the midpoint of a and B now If you do this for C and B this line Would also have Make a circle would also have a circle that would touch point C and B So that would mean that if every point on both of these lines make a circle that touches these These two points that means the intersection will touch all three points. I think that's a Pretty simple argument to follow after that After we find the center point, let's call this R big R After we find that in order to find the radius We would just need to find the distance between between the center point and one of these other points And it doesn't matter which one because the definition is that it's the same distance for all of them so that would just be Let's see let's say it's comprised of Rx and Ry the center point and You know, let's do a is ax and a y So It would just look like this. I think it was Rx minus ax Squared actually let me check Yeah, it's Rx minus ax squared plus Ry minus a y squared This is because of the simple of the Pythagorean theorem, which is a squared plus b squared Equal c squared So if we have like this point in this point and we want to make a circle This is length a this is length B the hypotenuse that would be the radius C and You know length a would be this Minus The y value of the first point minus the y value of the second point and the x value of the first point minus the x value of the second point and it wouldn't really matter because you're if it's negative because you're squaring it anyway so that would make it positive and If you know the standard unit circle thing So it would be x squared plus y squared Equals r squared so we don't even need to do like a square root to find to find see we can just leave it like Like this We can just leave it in that at that in that form rx minus ax squared plus r y minus a y squared and That's what I did here this if you can You can see this what this is the equation of the circle and this was the center of the circle big R The way I named my variables was really inconsistent. So So yeah, I Tried I did this on paper. I think the conic the way you do it with systems of equations with conics It's probably easier maybe easier I'm not sure I don't do these I haven't done the conic thing in a while But I imagine it would be easier than finding the slope than the Inverse line, but I think this is cool. I think it's a pretty simple argument and Yeah, it's just a quick video. I don't really have anything interesting that I'm Learning that I want to make a video on so I think that's all I might I might Might make a video on how to get a copy paste working on you of him And you know the C tutorial thing like I said, I'm not sure if I'm Proficient enough with C to make a tutorial Or at least a good tutorial Yeah, that's all