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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.

Language:
English Language

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.

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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