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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.

## Want to join the conversation?

- 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:

https://www.khanacademy.org/math/geometry/triangle-properties/angle_bisectors/v/incenter-and-incircles-of-a-triangle

And here is a picture of what it would look like:

http://www.mathwords.com/i/i_assets/incircle.jpg

Hope it helps!(13 votes)

- Does it matter where you put the straightedges to line it up to the triangle?(6 votes)
- untill and unless you can not get your task completed(2 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)
- He would plan ahead ofc(1 vote)

- 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 you please explain more(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)

## 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.