[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.86,0:00:05.47,Default,,0000,0000,0000,,Angle A is a circumscribed\Nangle on circle O.
Dialogue: 0,0:00:05.47,0:00:07.95,Default,,0000,0000,0000,,So this is angle\NA right over here.
Dialogue: 0,0:00:07.95,0:00:11.36,Default,,0000,0000,0000,,Then when they say it's\Na circumscribed angle,
Dialogue: 0,0:00:11.36,0:00:13.55,Default,,0000,0000,0000,,that means that the\Ntwo sides of the angle
Dialogue: 0,0:00:13.55,0:00:15.82,Default,,0000,0000,0000,,are tangent to the circle.
Dialogue: 0,0:00:15.82,0:00:18.53,Default,,0000,0000,0000,,So AC is tangent to\Nthe circle at point
Dialogue: 0,0:00:18.53,0:00:23.09,Default,,0000,0000,0000,,C. AB is tangent to\Nthe circle at point B.
Dialogue: 0,0:00:23.09,0:00:25.44,Default,,0000,0000,0000,,What is the measure of angle A?
Dialogue: 0,0:00:25.44,0:00:28.73,Default,,0000,0000,0000,,Now, I encourage you\Nto pause the video now
Dialogue: 0,0:00:28.73,0:00:30.84,Default,,0000,0000,0000,,and to try this out on your own.
Dialogue: 0,0:00:30.84,0:00:32.60,Default,,0000,0000,0000,,And I'll give you a hint.
Dialogue: 0,0:00:32.60,0:00:35.96,Default,,0000,0000,0000,,It will leverage the fact that\Nthis is a circumscribed angle
Dialogue: 0,0:00:35.96,0:00:38.58,Default,,0000,0000,0000,,as you could imagine.
Dialogue: 0,0:00:38.58,0:00:41.14,Default,,0000,0000,0000,,So I'm assuming you've\Ngiven a go at it.
Dialogue: 0,0:00:41.14,0:00:42.56,Default,,0000,0000,0000,,So the other piece\Nof information
Dialogue: 0,0:00:42.56,0:00:45.49,Default,,0000,0000,0000,,they give us is that angle D,\Nwhich is an inscribed angle,
Dialogue: 0,0:00:45.49,0:00:50.96,Default,,0000,0000,0000,,is 48 degrees and it intercepts\Nthe same arc-- so this
Dialogue: 0,0:00:50.96,0:00:53.94,Default,,0000,0000,0000,,is the arc that it intercepts,\Narc CB I guess you could call
Dialogue: 0,0:00:53.94,0:00:56.64,Default,,0000,0000,0000,,it-- it intercepts this\Narc right over here.
Dialogue: 0,0:00:56.64,0:00:57.74,Default,,0000,0000,0000,,It's the inscribed angle.
Dialogue: 0,0:00:57.74,0:01:02.32,Default,,0000,0000,0000,,The central angle that\Nintersects that same arc
Dialogue: 0,0:01:02.32,0:01:04.84,Default,,0000,0000,0000,,is going to be twice\Nthe inscribed angle.
Dialogue: 0,0:01:04.84,0:01:07.24,Default,,0000,0000,0000,,So this is going\Nto be 96 degrees.
Dialogue: 0,0:01:07.24,0:01:09.61,Default,,0000,0000,0000,,I could put three markers here\Njust because we've already
Dialogue: 0,0:01:09.61,0:01:11.37,Default,,0000,0000,0000,,used the double marker.
Dialogue: 0,0:01:11.37,0:01:15.86,Default,,0000,0000,0000,,Notice, they both intercept\Narc CB so some people would
Dialogue: 0,0:01:15.86,0:01:18.53,Default,,0000,0000,0000,,say the measure of\Narc CB is 96 degrees,
Dialogue: 0,0:01:18.53,0:01:21.18,Default,,0000,0000,0000,,the central angle is 96\Ndegrees, the inscribed angle
Dialogue: 0,0:01:21.18,0:01:23.57,Default,,0000,0000,0000,,is going to be half\Nof that, 48 degrees.
Dialogue: 0,0:01:23.57,0:01:25.85,Default,,0000,0000,0000,,So how does this help us?
Dialogue: 0,0:01:25.85,0:01:29.56,Default,,0000,0000,0000,,Well, a key clue is that angle\Nis a circumscribed angle.
Dialogue: 0,0:01:29.56,0:01:34.41,Default,,0000,0000,0000,,So that means AC and AB are\Neach tangent to the circle.
Dialogue: 0,0:01:34.41,0:01:37.45,Default,,0000,0000,0000,,Well, a line that is\Ntangent to the circle
Dialogue: 0,0:01:37.45,0:01:40.83,Default,,0000,0000,0000,,is going to be perpendicular to\Nthe radius of the circle that
Dialogue: 0,0:01:40.83,0:01:44.57,Default,,0000,0000,0000,,intersects the circle\Nat the same point.
Dialogue: 0,0:01:44.57,0:01:49.93,Default,,0000,0000,0000,,So this right over here is\Ngoing to be a 90-degree angle,
Dialogue: 0,0:01:49.93,0:01:53.73,Default,,0000,0000,0000,,and this right over here is\Ngoing to be a 90-degree angle.
Dialogue: 0,0:01:53.73,0:01:56.38,Default,,0000,0000,0000,,OC is perpendicular to CA.
Dialogue: 0,0:01:56.38,0:02:00.33,Default,,0000,0000,0000,,OB, which is a radius,\Nis perpendicular to BA,
Dialogue: 0,0:02:00.33,0:02:03.16,Default,,0000,0000,0000,,which is a tangent line, and\Nthey both intersect right
Dialogue: 0,0:02:03.16,0:02:06.52,Default,,0000,0000,0000,,over here at B. Now, this\Nmight jump out at you.
Dialogue: 0,0:02:06.52,0:02:08.51,Default,,0000,0000,0000,,We have a quadrilateral\Ngoing on here.
Dialogue: 0,0:02:08.51,0:02:13.48,Default,,0000,0000,0000,,ABOC is a quadrilateral,\Nso its sides
Dialogue: 0,0:02:13.48,0:02:20.31,Default,,0000,0000,0000,,are going to add\Nup to 360 degrees.
Dialogue: 0,0:02:20.31,0:02:23.17,Default,,0000,0000,0000,,So we could know, we\Ncould write it this way.
Dialogue: 0,0:02:23.17,0:02:26.38,Default,,0000,0000,0000,,We could write the\Nmeasure of angle A
Dialogue: 0,0:02:26.38,0:02:37.93,Default,,0000,0000,0000,,plus 90 degrees plus another\N90 degrees plus 96 degrees
Dialogue: 0,0:02:37.93,0:02:40.88,Default,,0000,0000,0000,,is going to be equal\Nto 360 degrees.
Dialogue: 0,0:02:46.62,0:02:49.72,Default,,0000,0000,0000,,Or another way of thinking\Nabout it, if we subtract 180
Dialogue: 0,0:02:49.72,0:02:52.67,Default,,0000,0000,0000,,from both sides, if we\Nsubtract that from both sides,
Dialogue: 0,0:02:52.67,0:02:59.87,Default,,0000,0000,0000,,we get the measure of\Nangle A plus 96 degrees
Dialogue: 0,0:02:59.87,0:03:05.14,Default,,0000,0000,0000,,is going to be equal\Nto 180 degrees.
Dialogue: 0,0:03:05.14,0:03:06.60,Default,,0000,0000,0000,,Or another way of\Nthinking about it
Dialogue: 0,0:03:06.60,0:03:09.95,Default,,0000,0000,0000,,is the measure of angle A\Nor that angle A and angle O
Dialogue: 0,0:03:09.95,0:03:12.86,Default,,0000,0000,0000,,right over here-- you\Ncould call it angle COB--
Dialogue: 0,0:03:12.86,0:03:15.62,Default,,0000,0000,0000,,that these are going to be\Nsupplementary angles if they
Dialogue: 0,0:03:15.62,0:03:18.99,Default,,0000,0000,0000,,add up to 180 degrees.
Dialogue: 0,0:03:18.99,0:03:22.13,Default,,0000,0000,0000,,So if we subtract 96\Ndegrees from both sides,
Dialogue: 0,0:03:22.13,0:03:27.56,Default,,0000,0000,0000,,we get the measure\Nof angle A is equal
Dialogue: 0,0:03:27.56,0:03:30.06,Default,,0000,0000,0000,,to-- I don't want to make that\Nlook like a less than symbol,
Dialogue: 0,0:03:30.06,0:03:32.38,Default,,0000,0000,0000,,let make it-- measure of\Nangle-- this one actually
Dialogue: 0,0:03:32.38,0:03:35.01,Default,,0000,0000,0000,,looks more like a--\Nmeasure of angle A
Dialogue: 0,0:03:35.01,0:03:37.98,Default,,0000,0000,0000,,is equal to 180 minus 96.
Dialogue: 0,0:03:37.98,0:03:39.84,Default,,0000,0000,0000,,Let's see, 180 minus\N90 would be 90,
Dialogue: 0,0:03:39.84,0:03:46.19,Default,,0000,0000,0000,,and then we subtract another\N6 gets us to 84 degrees.