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PROBLEM: "Construct a circle

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inscribing the triangle."

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So this would be a circle that's inside this triangle,

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where each of the sides of the triangle

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are tangents to the circle.

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And the one way to –

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Probably the easiest way to think about it is

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the center of that circle is going to be

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at the in center of the triangle.

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Now what is the in center of the triangle?

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The in center of the triangle is the intersection

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of the angle bisectors.

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So if I were to make a line

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that perfectly splits an angle in two –

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(So I'm eyeballing it right over here.)

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– this would be an angle bisector.

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But to be a little bit more precise about

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angle bisectors, I could actually use a compass.

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So let me make this a little bit smaller.

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And what I can do is I could put this –

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the center of the circle –

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on one of the sides of this angle right over here.

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Now let me get another circle.

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And I want to make it the same size.

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So let me center it there.

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I want to make it the exact same size.

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And now let me put it on the other one,

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on the other side of this angle.

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I'll put it right over here.

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And I want to put it so that the center of the circle

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is on the other side of the angle –

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and the circle itself – or the vertex –

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sits on the circle itself.

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And what this does is

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I can now look at the intersection of this point –

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the vertex – and this point,

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and that's going to be the angle bisector.

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So I am going to go through there,

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and I am going to go through there.

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Now let me move these circles over to here,

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so I can take the angle bisector of this side as well

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So I can put this one over here.

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And I could put this one –

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Let's see, I want to be on the side of the angle.

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And I want to go right through –

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I want the circle to go right through the vertex.

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Now let me add another straight edge here.

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So I want to go throgh this point

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and I want to bisect the angle and go right through

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the other point of intersection of these two circles.

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

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(I don't need that anymore.)

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– and let me use this one to actually construct

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the circle inscribing the triangle.

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

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And actually, this one's already pretty close,

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in terms of dimensions.

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And with this tool,

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

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It has some margin for error.

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And so, let's just go with this.

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This actually should be touching.

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But this has some margin for error.

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Let's see if this was good enough. It was.