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Inscribed Angles 1214 Views
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Description:
We inscribed some angles on the walls of our office, but our boss got mad, so we made this video instead.
Transcript
- 00:04
Inscribed Angles, a la Shmoop.
- 00:07
You’re at a friend’s house with three other friends and you decide to order an extra-large
- 00:11
pepperoni pizza from Inconvenient Pizzas, Inc…
- 00:15
…because their commercials say their prices are "Unbeatably Low!"
- 00:21
Two hours later than promised, your pizza is delivered.
Full Transcript
- 00:25
Like all pizzas from Inconvenient, your pizza is entirely whole and uncut.
- 00:30
Since there are 360 degrees in a circle and you each want an equal slice, you say:
- 00:36
"Okay guys, let's each cut our own slice.
- 00:39
We'll cut an angle that intercepts an arc of 90 degrees."
- 00:43
You mark four points 90 degrees of arc away from each other.
- 00:49
Your friend Wise Guy Louie is in charge of cutting the first slice…
- 00:54
…and just to make things difficult, he cuts it like this.
- 00:57
"Wise Guy Louie!" you all exclaim.
- 01:00
"What?" he says. "I did just what you told me."
- 01:03
As infuriating as he is, Wise Guy Louie is right.
- 01:06
Arc AB, which is indeed intercepted by the angle he cut, still has a measure of 90 degrees.
- 01:14
Instead of cutting a central angle as you expected him to, he cut an inscribed angle.
- 01:21
If an angle has its vertex on a circle
- 01:24
and has sides containing two chords of the same circle…
- 01:28
…then the angle is inscribed in that circle.
- 01:33
While you and your friends understandably find inscribed angles annoying,
- 01:37
they have some interesting properties.
- 01:40
We know that Wise Guy Louie's angle intercepted an arc of measure 90 degrees,
- 01:44
but can we find the measure of the angle?
- 01:47
The inscribed angle theorem tells us that the angle measure of AQB equals
- 01:52
½ times the measure of the arc AB.
- 01:57
Given that the arc’s measure AB is 90 degrees, we can multiply ½ times 90, to get 45 degrees.
- 02:06
Well, that’s doesn’t help. Wise Guy Louie still got the biggest slice.
- 02:09
Turns out inviting him was the most inconvenient thing that’s happened all evening.
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