In the figure shown, points P and Q lie on the circle with center O. What is the value of s?




A) 1/2
B) 1
C) Radical 2
D) Radical 3
E) (Radical 2)/2

OP = OQ
(1-0)^2 + (-sqrt3-0)^2 = (s-0)^2 + (t-0)^2
1+3 = s^2+t^2

s^2+t^2 = 4 ---------(1)


Since the lines are perpendicular to each other, product of slopes = -1
[(1-0)/(-sqrt3-0)]*[(t-0)/(s-0)] = -1
t/s = sqrt3
t = s*sqrt3
From (1), s^2 + 3s^2 = 4
s^2 = 1
Since (s,t) is in first quadrant, s=1

Good explanation! 1 is the correct answer.

I don't understand this explanation at all. Can someone help out?

GMAT Prep says the answer to this one is radical 3. I'm assuming they screwed up on this one and the correct answer is indeed "1". Can anyone help corroborate this? Thx!

Ignore the previous post. GMAT Prep says the answer is indeed "1." If someone can punch out an explanation that makes sense to those of us not fluent in PASCAL, it would be most appreciated!

there is a very thorough treatment of this problem here.