ShmoopTube

Where Monty Python meets your 10th grade teacher.

Search Thousands of Shmoop Videos


Math III Videos 103 videos

Unit Rate
20718 Views

Approximately 874 people per day wonder what a unit rate is. If you're one of them, check out our video on unit rates and how to use them. (We just...

Solving Proportions Using Cross Products
6802 Views

This video covers how to use cross products to solve for a missing number in a proportion by setting that proportion with a variable over the produ...

GED Math 2.4 Rational Numbers
190 Views

GED Math 2.4 Rational Numbers. Lucius's favorite restaurant is how many km from his home?

See All

SAT Math 3.1 Geometry and Measurement 194 Views


Share It!


Description:

SAT Math 3.1 Geometry and Measurement

Language:
English Language

Transcript

00:02

Here’s your shmoop du jour, brought to you by circle diagrams.

00:07

Leave your dirty minds at the door, please.

00:11

In this figure, O1 and O2 are circles with equal radii of 4 centimeters.

00:17

Find the length of the tangent O2P.

00:20

And here are the potential answers:

00:23

O2P or not to pee, that is the question.

00:28

So no matter how much this problem tries to fool us into thinking it’s about circles…

00:32

…we know it’s really a triangle problem.

00:35

Okay, so it’s missing a leg, so let’s go ahead and draw in that missing leg right now…

00:39

but be careful, we’re not drawing it straight up to the end of the line… only to the letter “P”…

00:44

Now, by property of a tangent, the radius O1 P has to be perpendicular to O2 P…

00:51

…making O1 P O2 a right triangle.

00:56

And whenever we have a right triangle… we can always call in our good friend Pythagoras

00:59

to help us out of our jam.

01:02

So (O1P)2 + (O2P)2 = (O1O2)2

01:06

We’re looking for O2 P, so we don’t know that one yet… but we can plug in the other

01:11

values because we’re told that the radius of both circles is 4.

01:16

So… O2 P squared plus 4 squared = 8 squared…or O2 P squared plus 16 = 64.

01:23

Subtract 16 from both sides, and O2 P squared = 48…

01:27

…which, after we take the square root of both sides,

01:29

reduces to the square root of 3 times 16, and we can take the root of 16 and pull it out of there….

01:37

…leaves us with 4 square root of 3 – answer C.

Related Videos

SAT Math 2.1 Geometry and Measurement
2779 Views

SAT Math 2.1 Geometry and Measurement. What is the measure of angle z in terms of x and y?

SAT Math 9.4 Algebra and Functions
1300 Views

SAT Math 9.4 Algebra and Functions

SAT Math 9.2 Algebra and Functions
377 Views

SAT Math 9.2 Algebra and Functions

SAT Math: Identifying an Equation for the Average of Two Percentages
23 Views

In 2014, the unemployment rate of one county in California was 7%. In another county, the unemployment rate was 11%. Which of the following express...

SAT Math: Which Equation Represents Profit?
13 Views

Angela is making cookies for a bake sale. She expects each batch of her cookies to sell for $40. It costs her $10 to make one batch of cookies, and...