QR DS 99

[jeffgmat]

I had a question about Data Sufficiency #99 in the Quantitative Review (2nd ed.) book.

I remember in an earlier practice question that had to do with a circle on a coordinate plane that we were able to find the radius of the circle because we knew that the distance from the center of the circle to coordinate (0,0) (i.e. the point at which two lines tangent to the circle intersect) was r/sqrt(2). Why does this logic not apply to this problem? If we know that the distance from the circle's center is 20, and we know the process for obtaining the side of a square (which is equal to the diameter, or 2r) from that number, why can we not use that in this problem to deduce the radius and, therefore, the distance from the center of the circle to point A?

I don't understand!!

[tim]

OG is a banned source; it is illegal to post OG questions anywhere on the web. If you are in one of our classes, please ask OG questions during office hours or before/after class..

[jeffgmat]

I'm not registered for a course but I bought all of the books.

How about a general math question then. This is worded kind of poorly but try to stay with me if you can:

If you have a circle with two lines tangent to it (that intersect to make it partially an inscribed circle), is there a way to find the radius of the circle if you only know the distance from the center of the circle to the intersection point for the two tangent lines? Is it not, in general, the formula for getting the length of a side of a square or a rhombus from the diagonal of a square or rhombus divided by two (as the length for the side of the square = diameter of the circle)?

If you CAN use these formulas, how do you delineate whether to use the formula for the square or the rhombus?

[jlucero]

I'm not registered for a course but I bought all of the books.

How about a general math question then. This is worded kind of poorly but try to stay with me if you can:

If you have a circle with two lines tangent to it (that intersect to make it partially an inscribed circle), is there a way to find the radius of the circle if you only know the distance from the center of the circle to the intersection point for the two tangent lines? Is it not, in general, the formula for getting the length of a side of a square or a rhombus from the diagonal of a square or rhombus divided by two (as the length for the side of the square = diameter of the circle)?

If you CAN use these formulas, how do you delineate whether to use the formula for the square or the rhombus?

No, you can not find the length of the radius from this information. The difference is that when a circle is inscribed within a square, you also know something about the ANGLE at which the two lines meet. Without knowing anything about angles, you can't determine a radius. For example, imagine two lines tangent to your circle that swivel and connect either closer or further from the circle. You can change the distance between the center of the circle at the intersection of the lines without changing the radius of the circle.