SAT Math 9.3 Geometry and Measurement
|Additional Topics in Math||Circles in the coordinate plane|
Equations of Circles
|Product Type||SAT Math|
|SAT Math||Geometry and Measurement|
All right, so we’ve got a bug on the move.
Any time we have a problem like this, we should be thinking in terms of a full circle.
In other words, we’re probably not going to be able to find the exact measure of just this little arc…
…without first finding the circumference of the entire circle…
…and then just taking 1/4 of that.
So…how do we find the circumference of the circle?
Well, first, we need the diameter. If we draw a line from H to J we get one…
now we just need to find its value…
Because we’re dealing with a square, we know we have right angles,
and the other two angles of our new triangle must be equal.
So…we’ve got a 45-45-90 triangle…sweet.
45-45-90 triangles have side lengths with a ratio of x to x to x square root of 2…
…so, if we’re taking the square root of 2 times the square root of 2, we wind up with just… plain ol’ 2.
So yeah, that's our diameter... 2.
Now all we have to do is plug that into our circumference formula of pi times the diameter…
…and we get 2 pi.
One-fourth of that is 1/2 pi… which is choice B.
As in, “Bugged.”