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Geometry and Measurement Videos 88 videos

SAT Math 1.1 Geometry and Measurement
719 Views

SAT Math 1.1 Geometry and Measurement. What is the circumference of the circle?

SAT Math 1.2 Geometry and Measurement
246 Views

SAT Math: Geometry and Measurement Drill 1, Problem 2. If A = (0, 4), B = (-3, 2), and C = (1, 0), which point is in the interior of angle ABC?

SAT Math 2.3 Geometry and Measurement
267 Views

SAT Math 2.3 Geometry and Measurement. Find the length of AB.

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SAT Math 9.3 Geometry and Measurement 194 Views


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Description:

SAT Math 9.3 Geometry and Measurement

Language:
English Language

Transcript

00:03

Here’s your shmoop du jour, brought to you by bugs. Not the rabbit kind.

00:09

A square with side lengths of square root of 2 is circumscribed into a circle.

00:14

A bug, traveling along the perimeter of the circle, moves from Point K to Point H.

00:20

How far did the bug travel?

00:22

Here are the potential answers...

00:26

All right, so we’ve got a bug on the move.

00:29

Any time we have a problem like this, we should be thinking in terms of a full circle.

00:33

In other words, we’re probably not going to be able to find the exact measure of just this little arc…

00:38

…without first finding the circumference of the entire circle…

00:41

…and then just taking 1/4 of that.

00:45

So…how do we find the circumference of the circle?

00:48

Well, first, we need the diameter. If we draw a line from H to J we get one…

00:55

now we just need to find its value…

00:57

Because we’re dealing with a square, we know we have right angles,

01:00

and the other two angles of our new triangle must be equal.

01:05

So…we’ve got a 45-45-90 triangle…sweet.

01:10

45-45-90 triangles have side lengths with a ratio of x to x to x square root of 2…

01:16

…so, if we’re taking the square root of 2 times the square root of 2, we wind up with just… plain ol’ 2.

01:21

So yeah, that's our diameter... 2.

01:24

Now all we have to do is plug that into our circumference formula of pi times the diameter…

01:29

…and we get 2 pi.

01:30

One-fourth of that is 1/2 pi… which is choice B.

01:34

As in, “Bugged.”

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