PROBLEM: "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 tangents to the circle.

And the one way to –

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 two –

(So I'm eyeballing 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 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.

And 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 the angle bisector.

So I am going to go through there,

and I am going to go through there.

Now let me move these circles over 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 –

Let's 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.

Now let me add another straight edge here.

So I want to go throgh this point

and I want to bisect the angle and go right through

the other point of intersection of these two circles.

Now let me get rid of one of these two circles –

(I don't need that anymore.)

– and let me use this one to actually construct

the circle inscribing the triangle.

So I'm to going put it at the center right over there.

And actually, this one's already pretty close,

in terms of dimensions.

And with this tool,

you don't have to be a hundred percent precise.

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.