SAT Math 9.3 Geometry and Measurement

SAT Math 9.3 Geometry and Measurement

Additional Topics in MathCircles in the coordinate plane
CirclesCircumference
Equations of Circles
GeometryCircles
LanguageEnglish Language
Product TypeSAT Math
SAT MathGeometry and Measurement

Transcript

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.”