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# Geometric constructions: triangle-circumscribing circle

## 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 which is or a virtual compass and a virtual straightedge 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 make us 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 then this allows us to construct a perpendicular bisector if I go through that point and this point right over here this bisects that's bisects 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 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 straightedge 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 that's the perpendicular bisector of this side right over here and I could do the third side and it would intersect 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 Center 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 you to they really want to see that you've made it at drawing the perpendicular bisectors of the sides to find the circumcenter and then you put a circle right over there