ShmoopTube

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.”

Full Transcript