Source: Revised GRE PDF 1st Ed. Section 5: Math; #6 (p. 72)

10

O is the center of the circle

O is the center of the circle, and the perimeter of AOB is 6. Quantity A : The circumference of the circle Quantity B : 12 Quantity A is greater., Quantity B is greater., The two quantities are equal., The relationship cannot be determined from the information given.

3 Explanations

1

How can we assume its an equilateral triangle without being told? The other two angles can be any variation that add up to 180

Dec 1, 2018 • Comment

David Recine, Magoosh Tutor

That's a great question. You're correct that simply knowing we have one 60 degree angle (as seen in the figure) is not enough.

However, if a triangle has one 60 degree angle, AND the two sides of that angle are equal, then two opposite angles (angles A and B in the figure) will also be 60 degrees.

And of course, if all angles are equal, then all sides will be equal.

Dec 5, 2018 • Reply

3

Hi Chris,

I have a question, I second-guessed this problem because in other problems kind of like this with triangles they always say to not assume the image is correct unless told otherwise. How can we assume that points A and B will like on the circle and can't be moved since it doesn't say the image is correct or that OA/OB are radii?

Thanks

Jun 26, 2016 • Comment

Sam Kinsman, Magoosh Tutor

Thanks for asking about this! You're right that we should not assume that diagrams are drawn to scale. Just because one area looks larger than another doesn't mean it is.

We don't need to get too suspicious, however :-) The GRE marks the endpoints correctly in its diagrams. If the diagram makes it look like points A and B are on the circle, then they are. The GRE writers will not trick you by giving you a line that looks like it ends in a certain place, but actually goes farther.

Jun 27, 2016 • Reply

2 Chris Lele, Magoosh Tutor

Sep 26, 2012 • Comment