[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.40,0:00:01.66,Default,,0000,0000,0000,,PROBLEM: "Construct a circle
Dialogue: 0,0:00:01.66,0:00:03.20,Default,,0000,0000,0000,,inscribing the triangle."
Dialogue: 0,0:00:03.20,0:00:06.48,Default,,0000,0000,0000,,So this would be a circle that's inside this triangle,
Dialogue: 0,0:00:06.48,0:00:08.93,Default,,0000,0000,0000,,where each of the sides of the triangle
Dialogue: 0,0:00:08.93,0:00:11.87,Default,,0000,0000,0000,,are tangents to the circle.
Dialogue: 0,0:00:11.87,0:00:14.26,Default,,0000,0000,0000,,And the one way to –
Dialogue: 0,0:00:14.26,0:00:16.33,Default,,0000,0000,0000,,Probably the easiest way to think about it is
Dialogue: 0,0:00:16.33,0:00:18.98,Default,,0000,0000,0000,,the center of that circle is going to be
Dialogue: 0,0:00:18.98,0:00:20.96,Default,,0000,0000,0000,,at the in center of the triangle.
Dialogue: 0,0:00:20.96,0:00:22.68,Default,,0000,0000,0000,,Now what is the in center of the triangle?
Dialogue: 0,0:00:22.68,0:00:26.07,Default,,0000,0000,0000,,The in center of the triangle is the intersection
Dialogue: 0,0:00:26.07,0:00:28.87,Default,,0000,0000,0000,,of the angle bisectors.
Dialogue: 0,0:00:28.87,0:00:31.88,Default,,0000,0000,0000,,So if I were to make a line
Dialogue: 0,0:00:31.88,0:00:34.98,Default,,0000,0000,0000,,that perfectly splits an angle in two –
Dialogue: 0,0:00:34.98,0:00:36.28,Default,,0000,0000,0000,,(So I'm eyeballing it right over here.)
Dialogue: 0,0:00:36.28,0:00:38.28,Default,,0000,0000,0000,,– this would be an angle bisector.
Dialogue: 0,0:00:38.28,0:00:40.21,Default,,0000,0000,0000,,But to be a little bit more precise about
Dialogue: 0,0:00:40.21,0:00:42.79,Default,,0000,0000,0000,,angle bisectors, I could actually use a compass.
Dialogue: 0,0:00:42.79,0:00:45.12,Default,,0000,0000,0000,,So let me make this a little bit smaller.
Dialogue: 0,0:00:45.12,0:00:47.19,Default,,0000,0000,0000,,And what I can do is I could put this –
Dialogue: 0,0:00:47.19,0:00:48.48,Default,,0000,0000,0000,,the center of the circle –
Dialogue: 0,0:00:48.48,0:00:52.95,Default,,0000,0000,0000,,on one of the sides of this angle right over here.
Dialogue: 0,0:00:52.95,0:00:55.22,Default,,0000,0000,0000,,Now let me get another circle.
Dialogue: 0,0:00:55.22,0:00:57.32,Default,,0000,0000,0000,,And I want to make it the same size.
Dialogue: 0,0:00:57.32,0:00:59.28,Default,,0000,0000,0000,,So let me center it there.
Dialogue: 0,0:00:59.28,0:01:01.71,Default,,0000,0000,0000,,I want to make it the exact same size.
Dialogue: 0,0:01:01.71,0:01:03.68,Default,,0000,0000,0000,,And now let me put it on the other one,
Dialogue: 0,0:01:03.68,0:01:06.25,Default,,0000,0000,0000,,on the other side of this angle.
Dialogue: 0,0:01:06.25,0:01:08.43,Default,,0000,0000,0000,,I'll put it right over here.
Dialogue: 0,0:01:08.43,0:01:10.20,Default,,0000,0000,0000,,And I want to put it so that the center of the circle
Dialogue: 0,0:01:10.20,0:01:12.32,Default,,0000,0000,0000,,is on the other side of the angle –
Dialogue: 0,0:01:12.32,0:01:14.19,Default,,0000,0000,0000,,and the circle itself – or the vertex –
Dialogue: 0,0:01:14.19,0:01:16.26,Default,,0000,0000,0000,,sits on the circle itself.
Dialogue: 0,0:01:16.26,0:01:17.23,Default,,0000,0000,0000,,And what this does is
Dialogue: 0,0:01:17.23,0:01:19.43,Default,,0000,0000,0000,,I can now look at the intersection of this point –
Dialogue: 0,0:01:19.43,0:01:21.14,Default,,0000,0000,0000,,the vertex – and this point,
Dialogue: 0,0:01:21.14,0:01:24.67,Default,,0000,0000,0000,,and that's going to be the angle bisector.
Dialogue: 0,0:01:24.67,0:01:26.20,Default,,0000,0000,0000,,So I am going to go through there,
Dialogue: 0,0:01:26.20,0:01:29.14,Default,,0000,0000,0000,,and I am going to go through there.
Dialogue: 0,0:01:29.14,0:01:33.40,Default,,0000,0000,0000,,Now let me move these circles over to here,
Dialogue: 0,0:01:33.40,0:01:37.43,Default,,0000,0000,0000,,so I can take the angle bisector of this side as well
Dialogue: 0,0:01:37.43,0:01:39.41,Default,,0000,0000,0000,,So I can put this one over here.
Dialogue: 0,0:01:39.41,0:01:41.41,Default,,0000,0000,0000,,And I could put this one –
Dialogue: 0,0:01:41.41,0:01:43.42,Default,,0000,0000,0000,,Let's see, I want to be on the side of the angle.
Dialogue: 0,0:01:43.42,0:01:45.60,Default,,0000,0000,0000,,And I want to go right through –
Dialogue: 0,0:01:45.60,0:01:48.20,Default,,0000,0000,0000,,I want the circle to go right through the vertex.
Dialogue: 0,0:01:48.20,0:01:50.60,Default,,0000,0000,0000,,Now let me add another straight edge here.
Dialogue: 0,0:01:50.60,0:01:52.66,Default,,0000,0000,0000,,So I want to go throgh this point
Dialogue: 0,0:01:52.66,0:01:57.46,Default,,0000,0000,0000,,and I want to bisect the angle and go right through
Dialogue: 0,0:01:57.46,0:02:01.07,Default,,0000,0000,0000,,the other point of intersection of these two circles.
Dialogue: 0,0:02:01.07,0:02:04.60,Default,,0000,0000,0000,,Now let me get rid of one of these two circles –
Dialogue: 0,0:02:04.60,0:02:06.26,Default,,0000,0000,0000,,(I don't need that anymore.)
Dialogue: 0,0:02:06.26,0:02:08.92,Default,,0000,0000,0000,,– and let me use this one to actually construct
Dialogue: 0,0:02:08.92,0:02:10.76,Default,,0000,0000,0000,,the circle inscribing the triangle.
Dialogue: 0,0:02:10.76,0:02:12.80,Default,,0000,0000,0000,,So I'm to going put it at the center right over there.
Dialogue: 0,0:02:12.80,0:02:14.78,Default,,0000,0000,0000,,And actually, this one's already pretty close,
Dialogue: 0,0:02:14.78,0:02:16.77,Default,,0000,0000,0000,,in terms of dimensions.
Dialogue: 0,0:02:16.77,0:02:17.60,Default,,0000,0000,0000,,And with this tool,
Dialogue: 0,0:02:17.60,0:02:20.27,Default,,0000,0000,0000,,you don't have to be a hundred percent precise.
Dialogue: 0,0:02:20.27,0:02:25.62,Default,,0000,0000,0000,,It has some margin for error.
Dialogue: 0,0:02:25.62,0:02:27.19,Default,,0000,0000,0000,,And so, let's just go with this.
Dialogue: 0,0:02:27.19,0:02:28.67,Default,,0000,0000,0000,,This actually should be touching.
Dialogue: 0,0:02:28.67,0:02:29.84,Default,,0000,0000,0000,,But this has some margin for error.
Dialogue: 0,0:02:29.84,0:02:32.35,Default,,0000,0000,0000,,Let's see if this was good enough. It was.