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## High school geometry

### Course: High school geometry>Unit 8

Lesson 12: Constructing circumcircles & incircles

# Geometric constructions: triangle-circumscribing circle

Sal constructs a circle that circumscribes a given triangle using compass and straightedge. Created by Sal Khan.

## Video transcript

Construct a circle circumscribing the triangle. So that would be a circle that touches the vertices, the three vertices of this triangle. So we can construct it using a compass and a straight edge, or a virtual compass and a virtual straight edge. So what we want to do is center the circle at the perpendicular bisectors of the sides, or sometimes that's called the circumcenter of this triangle. So let's do that. And so let's think about-- let's try to construct where the perpendicular bisectors of the sides are. So let me put a circle right over here whose radius is longer than this side right over here. Now let me get one that has the same size. So let me make it the same size as the one I just did. And let me put it right over here. And this allows us to construct a perpendicular bisector. If I go through that point and this point right over here, this bisects this side over here, and it's at a right angle. So now let's do that for the other sides. So if I move this over here-- and I really just have to do it for one of the other sides, because the intersection of two lines is going to give me a point. So I can do it for this side right over here. Let me scroll down so you can see a little bit clearer. So let me add another straight edge right over here. So I'm going to go through that point, and I'm going to go through this point. So that's the perpendicular bisector of this side right over here. And I could do the third side and it should intersect at that point. I'm not ultra, ultra precise, but I'm close enough. And now I just have to center one of these circles. Let me move one of these away. So let me just get rid of this one. And I just have to move this circle to the circumcenter and adjust its radius so that it gets pretty close to touching the three sides, the three vertices of this triangle. It doesn't have to be perfect. I think this exercise has some margin for error. But they really want to see that you've made an attempt at drawing the perpendicular bisectors of the sides, to find the circumcenter, and then you put a circle right over there.