[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.59,0:00:02.05,Default,,0000,0000,0000,,PROBLEM: "Construct a circle
Dialogue: 0,0:00:02.05,0:00:03.54,Default,,0000,0000,0000,,circumscribing the triangle."
Dialogue: 0,0:00:03.54,0:00:06.91,Default,,0000,0000,0000,,So that would be a circle that touches the vertices
Dialogue: 0,0:00:06.91,0:00:09.60,Default,,0000,0000,0000,,the three vertices of this triangle.
Dialogue: 0,0:00:09.60,0:00:12.70,Default,,0000,0000,0000,,So we can construct it using a compass
Dialogue: 0,0:00:12.70,0:00:14.58,Default,,0000,0000,0000,,and a straight edge, or a virtual compass
Dialogue: 0,0:00:14.58,0:00:15.78,Default,,0000,0000,0000,,and a virtual straight edge.
Dialogue: 0,0:00:15.78,0:00:17.09,Default,,0000,0000,0000,,So what we want to do is to center the circle
Dialogue: 0,0:00:17.09,0:00:20.74,Default,,0000,0000,0000,,at the perpendicular bisectors of the sides.
Dialogue: 0,0:00:20.74,0:00:21.70,Default,,0000,0000,0000,,Or sometimes that's called
Dialogue: 0,0:00:21.70,0:00:24.82,Default,,0000,0000,0000,,the 'circumcenter' of this triangle.
Dialogue: 0,0:00:24.82,0:00:27.06,Default,,0000,0000,0000,,So let's do that.
Dialogue: 0,0:00:27.06,0:00:29.57,Default,,0000,0000,0000,,And so let's think about –
Dialogue: 0,0:00:29.57,0:00:32.78,Default,,0000,0000,0000,,Let's try to construct where the perpendicular
Dialogue: 0,0:00:32.78,0:00:36.05,Default,,0000,0000,0000,,bisectors of the sides are.
Dialogue: 0,0:00:36.05,0:00:38.83,Default,,0000,0000,0000,,So let me put a circle right over here whose radius
Dialogue: 0,0:00:38.83,0:00:41.33,Default,,0000,0000,0000,,is longer than this side right over here.
Dialogue: 0,0:00:41.33,0:00:45.56,Default,,0000,0000,0000,,Now let me get one that has the same size.
Dialogue: 0,0:00:45.56,0:00:46.99,Default,,0000,0000,0000,,So let me make it the same size
Dialogue: 0,0:00:46.99,0:00:49.26,Default,,0000,0000,0000,,as the one I just did.
Dialogue: 0,0:00:49.26,0:00:51.46,Default,,0000,0000,0000,,And let me put it right over here.
Dialogue: 0,0:00:51.46,0:00:53.95,Default,,0000,0000,0000,,And this allows us to construct
Dialogue: 0,0:00:53.95,0:00:58.27,Default,,0000,0000,0000,,a perpendicular bisector.
Dialogue: 0,0:00:58.27,0:01:02.22,Default,,0000,0000,0000,,If I go through that point and this point right over here,
Dialogue: 0,0:01:02.22,0:01:06.16,Default,,0000,0000,0000,,this bisects this side over here,
Dialogue: 0,0:01:06.16,0:01:08.08,Default,,0000,0000,0000,,and it's at a right angle.
Dialogue: 0,0:01:08.08,0:01:10.02,Default,,0000,0000,0000,,So now let's do that for the other sides.
Dialogue: 0,0:01:10.02,0:01:12.66,Default,,0000,0000,0000,,So if I move this over here,
Dialogue: 0,0:01:12.66,0:01:14.96,Default,,0000,0000,0000,,and I really just have to do it for one of the other sides,
Dialogue: 0,0:01:14.96,0:01:17.44,Default,,0000,0000,0000,,because the intersection of two lines
Dialogue: 0,0:01:17.44,0:01:19.10,Default,,0000,0000,0000,,is going to give me a point.
Dialogue: 0,0:01:19.10,0:01:20.07,Default,,0000,0000,0000,,So I can do it
Dialogue: 0,0:01:20.07,0:01:21.41,Default,,0000,0000,0000,,for this side right over here.
Dialogue: 0,0:01:21.41,0:01:24.16,Default,,0000,0000,0000,,Let me scroll down so that you can see a bit clearer.
Dialogue: 0,0:01:24.16,0:01:27.10,Default,,0000,0000,0000,,So let me add another straight edge right over here.
Dialogue: 0,0:01:27.10,0:01:29.40,Default,,0000,0000,0000,,so I'm going to go through that point,
Dialogue: 0,0:01:29.41,0:01:31.62,Default,,0000,0000,0000,,and I'm going to go through this point.
Dialogue: 0,0:01:31.62,0:01:38.11,Default,,0000,0000,0000,,So that's the perpendicular bisector of
Dialogue: 0,0:01:38.11,0:01:39.52,Default,,0000,0000,0000,,this side right over here.
Dialogue: 0,0:01:39.52,0:01:41.59,Default,,0000,0000,0000,,And now I could do the third sided
Dialogue: 0,0:01:41.59,0:01:43.46,Default,,0000,0000,0000,,and it should intersect at that point.
Dialogue: 0,0:01:43.46,0:01:45.49,Default,,0000,0000,0000,,I'm not being ultra, ultra-precise.
Dialogue: 0,0:01:45.49,0:01:46.22,Default,,0000,0000,0000,,But I'm close enough.
Dialogue: 0,0:01:46.22,0:01:48.22,Default,,0000,0000,0000,,And now I just have to center one of these circles.
Dialogue: 0,0:01:48.22,0:01:50.66,Default,,0000,0000,0000,,Let me move one of these away.
Dialogue: 0,0:01:50.66,0:01:52.88,Default,,0000,0000,0000,,So let me just get rid of this one.
Dialogue: 0,0:01:52.88,0:01:55.32,Default,,0000,0000,0000,,And now I just have to move this circle
Dialogue: 0,0:01:55.32,0:01:58.66,Default,,0000,0000,0000,,to the circumcenter and adjust its radius so that
Dialogue: 0,0:01:58.66,0:02:03.14,Default,,0000,0000,0000,,it gets pretty close to touching the three sides,
Dialogue: 0,0:02:03.14,0:02:06.03,Default,,0000,0000,0000,,the three vertices of this triangle.
Dialogue: 0,0:02:06.03,0:02:07.23,Default,,0000,0000,0000,,It doesn't have to be perfect.
Dialogue: 0,0:02:07.23,0:02:09.27,Default,,0000,0000,0000,,I think this exercise has some margin for error.
Dialogue: 0,0:02:09.27,0:02:12.14,Default,,0000,0000,0000,,But they really want to see that you've made
Dialogue: 0,0:02:12.14,0:02:15.52,Default,,0000,0000,0000,,an attempt at drawing the perpendicular bisectors
Dialogue: 0,0:02:15.52,0:02:18.09,Default,,0000,0000,0000,,of the sides, and to find the circumcenter,
Dialogue: 0,0:02:18.09,0:02:21.47,Default,,0000,0000,0000,,and then you put a circle right over there.