High school geometry
Sal constructs a circle that circumscribes a given triangle using compass and straightedge. Created by Sal Khan.
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- How do you delete compasses and straight edges in the program?(7 votes)
- Hi there,
You can delete a single circle (compass) or a single segment (straightedge) in this exercise. The only option now is to click Clear to delete all of them.(13 votes)
- Would it be the same to bisect all the angles at1:02, instead of the sides?(1 vote)
- No, then you would construct something we call incentre and with incentre you can make circle that would "fit inside" the circle - incircle.
Here is a Khan Academy video about incircles:
And here is a picture of what it would look like:
Hope it helps!(13 votes)
- Does it matter where you put the straightedges to line it up to the triangle?(6 votes)
- Does the size of the compasses used to find the bisector matter? Or can you use any size?(2 votes)
- They need to have a radius equal to at least half of the triangle's side length. In addition, each compass needs to be the same size.
However, so long as you meet those requirements, they can be as big as you want.(3 votes)
- How does he know that what he does starting at0:38will make the correct perpendicular bisector?(3 votes)
- Why doesn't this seem to work with obtuse triangles?
I'm assigned to circumscribe an obtuse triangle, but it doesn't seem to be possible.(2 votes)
- Can we solve this question by finding the intersections of angle bisector like how Sal Khan did in (circle inscribing triangle) ?(2 votes)
- At1:18Sal puts his compass down but it jumps to the wrong point, he then uses it to bisect a line perpendicularly, is that right?(1 vote)
- Kind of. While it is not exactly precise, like he stated, the system is merely recognizing the general placement of lines and compasses to see that you attempted to find the correct circle. The result would be something similar to the right circle. So you would get it right on here.(2 votes)
- Can we use the same solution from "inscribing triangle"?(1 vote)
- No, because if one of the angles is obtuse, the circumcenter (the point where all the perpendicular bisectors intersect) will be outside of the circle. If you bisect the angles, they will always meet inside the triangle.(1 vote)
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.