two circles are separated

sanju09 wrote:Let the length of common tangents when two circles cut each other at a right angle be x. The length of common tangent when these two circles are separated so as to touch each other externally at one point only, is
(A) √2 x
(B) (√2 + 1)x
(C) √3 x
(D) (√3 + 1) x
(E) Cannot be determined

I have to admit, I have absolutely no clue what this question means. I've never seen the phrase "two circles cut each other at a right angle" and can only guess at how to draw this out.

"Circles cutting each other" means that they have exactly two points of intersection, and you can draw a straight line between those two points, but there's no internal angle. Perhaps "cut each other at a right angle" is supposed to mean that the line drawn from centre to centre is perpendicular to this straight line.

As for the length of common tangents, a tangent is a line that touches a circle at exactly one point. So, the common tangents would be lines that touch both circles at exactly one point. Nothing in the question suggests that the common tangent doesn't extend beyond those two points (a tangent can have infinite length), however, so there's too much ambiguity.

If you have a diagram to explain the question, please provide it. I'm guessing that this is not a real GMAT question - what's the source?

I have complained the same ambiguity to the source of this question, but the answer is still awaited. In fact all circles intersect each other normally. They have √2 x as the right answer to it. I am struggling in drawing the figure for this. It’s NOT a GMAT question; Stuart!!

sanju09 wrote:I have complained the same ambiguity to the source of this question, but the answer is still awaited. In fact all circles intersect each other normally. They have √2 x as the right answer to it. I am struggling in drawing the figure for this. It’s NOT a GMAT question; Stuart!!

Well, based on the x in the original and the answer of x√2, I'm guessing that it has something to do with constructing a 45/45/90 triangle (whose sides are in a ratio of x:x:x√2), but I really have no clue how to get that answer.

Honestly, I'd just write this question off - you'll never have to deal with this kind of translation nightmare on the real exam.

i eggry :mrgreen: