Two and three-point circles

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Transcript

In this video, let's think about circles. And points. When you draw a circle, it emanates from a center point, and it goes to some radius, that value that you set. Now if I want to draw a circle that goes through two points, I'll put two points on the screen here. And now I want a circle to go through those two points. To make that happen, I need to bisect the line implied by those two points.

I can do that with this tool. And that locates the center point. Now I can draw a circle from the center out to either one of the points and you can rest assured that the circle goes through both points because the center is in the middle of those two points. By definition, it's bisected. Now what happens if I want to draw a circle through three points. I'm gonna put three points arbitrarily on the screen.

Now that's a much harder challenge the solution Is to intersect two of the sides perpendicular bisectors. I'll do that here. I'll draw in the perpendicular bisector between those two points, and these two that will locate a center point, which I'll label right here is point A. Now if I draw a circle, from point A, you can have it go through any one of these three points. And you can rest assured that it will go through all three, it will be precisely tangent to those three points. So you can use this method.

Whenever you have a triangle of any sides, you want to have a circle circumscribe it, what you need to do is figure out where the center of the circle is by drawing in two perpendicular bisectors. That would be this point here, point B. Now I can draw a circle from B to one of the ends of the triangle and we've accomplished the goal There's even a specialized tool. For this purpose, I drawn three points. I can use this tool right here. Just tap on the three points.

And the app figures it out for you. But now you know how it's done. The traditional and the digital methods

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