In the figure above, points P and Q lie on the circle with center O. What is the value of s? A) 1/2 B) 1 C) sqrt(2) D) sqrt(3) E) sqrt(2)/2 OA is B

In the figure above, points P and Q lie on the circle with center O. What is the value of S? a) 1/2 b) 1 c) √2 d) √3 e) (√2)/2 Here's one approach: So, s = 1 Answer: B Cheers, Brent

vrn2vw wrote: In the figure above, points P and Q lie on the circle with center O. What is the value of s? a) 1/2 b) 1 c) √2 d) √3 e) (√2)/2 The slopes of perpendicular lines are the negative reciprocals of each other. So the slope of segment OQ is the negative reciprocal of the slope of segment OP. Since point O is the origin, and has coordinates (0, 0), we can easily calculate the slope of OP, which is -1/√3. So the slope of OQ is √3/1. Since OP and OQ are both radii of a circle, they are the same length. So, if OP goes across -√3 and up 1 in that length, then OQ, which lies in the first quadrant and has a slope the negative reciprocal of the slope of OP, must go across 1 and up √3. So the correct answer is B.

I took the long road using the distance formula Since OPQ is a right triangle OP^2 + OQ^2 = PQ^2 (√3^2 + 1^2) + (s^2 + t^2) = (s + √3)^2 + (t - 1)^2 4 + s^2 + t^2 = (s^2 + 3 + 2s√3) + (t^2 + 1 - 2t) 0 = 2s√3 - 2t s√3 = t s/t = 1/√3 s = 1 Answer B

Hi vrn2vw, Brent's approach to solving this question is exactly how I would have done it, so I won't rehash that explanation. Instead I'll point out the patterns and "hints" that were in the original drawing (and that you should be on the lookout for when dealing with similar questions). 1) Any time you see a diagonal line segment on a graph, you can draw a right triangle using that line as the hypoteneuse. 2) Right triangles on the GMAT are almost always pattern-based (angles or sides; at the very least, the Pythagorean Theorem). Here, we have a 1 and a √3, so we should be thinking 30/60/90. 3) Radii have the same length no matter what direction they go in. 4) Lines "add up" to 180 degrees. GMAT assassins aren't born, they're made, Rich

Rich.C@EMPOWERgmat.com wrote: Brent's approach to solving this question is exactly how I wouldn't have done it, so I ..... I think/hope you mean "would"

Hi Brent, HA. Yes, I did mean 'would' - I was clearly typing too fast! GMAT assassins aren't born, they're made, Rich

If I had a nickel for every time I've done that ... You haven't lived until you've written 2 + 2 = 22 on a board in front of 20+ talented students who've paid over $1000 to take your class! ._.