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# Geometric constructions: triangle-inscribing circle

CCSS.Math:

## Video transcript

construct a circle inscribing the triangle so this would be a circle that's inside this triangle where each of the sides of the triangle are tangent to the circle and one way to or the one the probably the easiest way to think about it is the center of that circle is going to be at the in center of the triangle now what is the in center of the triangle the in center of the triangle is the intersection of the angle bisectors so if I were to make a line that perfectly splits an angle in - so I'm a balling it right over here this would be an angle bisector but to be a little bit more precise about angle bisectors I could actually use a compass so let me make this a little bit smaller and what I can do is I could put this the center of the circle on one of the sides of this angle right over here now let me get another circle and I want to I want to make it the same size so let me Center it there I want to make it the exact same size and now let me put it on the other one on the other side of this angle I'll put it right over here I want to put it so that the center of the circle is on the other side of the angle and the circle itself or the vertex sits on the circle itself and what this does is I can now look at the intersection of this point the vertex and this point and that's going to be an angle bisector or the angle bisector so let me go I'm going to go through there and I'm going to go through there now let me move these circles over to to here so I can take the angle bisector of this side as well so I can put this one over here and I could put this one see I want to be on the side of the angle and I want to go right through I want the circle to go right through the vertex and let me add another straight edge here so I want to go through this point and I want to bisect the angle so I want to bisect the angle go right through the other point of intersection of these two circles now let me get rid of one of these let me get rid of one of these two circles I don't need it that anymore and let me use this one to actually construct the circle inscribing the triangle so I'm going put it at the center right over there actually this one's already pretty close in terms of dimensions and with this tool you don't have to be 100% precise it has some margin for error it has some margin for error and so let's just go with this this actually should be touching but this has some margin for error let's see if this was good enough it was