Constructing circumscribing circle

This video demonstrates on how to construct a circle circumscribing a triangle.

PROBLEM: "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 to 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 that you can see a 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 now I could do the third sided

and it should intersect at that point.

I'm not being 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 now 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, and to find the circumcenter,

and then you put a circle right over there.