0:00:00.000,0:00:00.860


0:00:00.860,0:00:05.470
Angle A is a circumscribed[br]angle on circle O.

0:00:05.470,0:00:07.950
So this is angle[br]A right over here.

0:00:07.950,0:00:11.360
Then when they say it's[br]a circumscribed angle,

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that means that the[br]two sides of the angle

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are tangent to the circle.

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So AC is tangent to[br]the circle at point

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C. AB is tangent to[br]the circle at point B.

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What is the measure of angle A?

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Now, I encourage you[br]to pause the video now

0:00:28.730,0:00:30.840
and to try this out on your own.

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And I'll give you a hint.

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It will leverage the fact that[br]this is a circumscribed angle

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as you could imagine.

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So I'm assuming you've[br]given a go at it.

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So the other piece[br]of information

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they give us is that angle D,[br]which is an inscribed angle,

0:00:45.490,0:00:50.960
is 48 degrees and it intercepts[br]the same arc-- so this

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is the arc that it intercepts,[br]arc CB I guess you could call

0:00:53.940,0:00:56.640
it-- it intercepts this[br]arc right over here.

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It's the inscribed angle.

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The central angle that[br]intersects that same arc

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is going to be twice[br]the inscribed angle.

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So this is going[br]to be 96 degrees.

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I could put three markers here[br]just because we've already

0:01:09.610,0:01:11.370
used the double marker.

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Notice, they both intercept[br]arc CB so some people would

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say the measure of[br]arc CB is 96 degrees,

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the central angle is 96[br]degrees, the inscribed angle

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is going to be half[br]of that, 48 degrees.

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So how does this help us?

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Well, a key clue is that angle[br]is a circumscribed angle.

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So that means AC and AB are[br]each tangent to the circle.

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Well, a line that is[br]tangent to the circle

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is going to be perpendicular to[br]the radius of the circle that

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intersects the circle[br]at the same point.

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So this right over here is[br]going to be a 90-degree angle,

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and this right over here is[br]going to be a 90-degree angle.

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OC is perpendicular to CA.

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OB, which is a radius,[br]is perpendicular to BA,

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which is a tangent line, and[br]they both intersect right

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over here at B. Now, this[br]might jump out at you.

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We have a quadrilateral[br]going on here.

0:02:08.509,0:02:13.480
ABOC is a quadrilateral,[br]so its sides

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are going to add[br]up to 360 degrees.

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So we could know, we[br]could write it this way.

0:02:23.170,0:02:26.380
We could write the[br]measure of angle A

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plus 90 degrees plus another[br]90 degrees plus 96 degrees

0:02:37.930,0:02:40.880
is going to be equal[br]to 360 degrees.

0:02:40.880,0:02:46.620


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Or another way of thinking[br]about it, if we subtract 180

0:02:49.720,0:02:52.670
from both sides, if we[br]subtract that from both sides,

0:02:52.670,0:02:59.870
we get the measure of[br]angle A plus 96 degrees

0:02:59.870,0:03:05.142
is going to be equal[br]to 180 degrees.

0:03:05.142,0:03:06.600
Or another way of[br]thinking about it

0:03:06.600,0:03:09.950
is the measure of angle A[br]or that angle A and angle O

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right over here-- you[br]could call it angle COB--

0:03:12.860,0:03:15.620
that these are going to be[br]supplementary angles if they

0:03:15.620,0:03:18.990
add up to 180 degrees.

0:03:18.990,0:03:22.130
So if we subtract 96[br]degrees from both sides,

0:03:22.130,0:03:27.561
we get the measure[br]of angle A is equal

0:03:27.561,0:03:30.060
to-- I don't want to make that[br]look like a less than symbol,

0:03:30.060,0:03:32.380
let make it-- measure of[br]angle-- this one actually

0:03:32.380,0:03:35.010
looks more like a--[br]measure of angle A

0:03:35.010,0:03:37.980
is equal to 180 minus 96.

0:03:37.980,0:03:39.840
Let's see, 180 minus[br]90 would be 90,

0:03:39.840,0:03:46.190
and then we subtract another[br]6 gets us to 84 degrees.

0:03:46.190,0:03:46.695