-
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.