gmat prep-----geometry

Ans B.

angle between -ve x-axis and OP is 30 degree because absolute value of x-coordinate is sqrt(3) and y-coordinate is 1.
that means angle between +ve x-axis and OQ is 60 degrees (90-30).
Now length of OP=OQ=2
so x-coordinate of OQ (i.e., s) must be 1 (2 * sin60).
hope this helps.

thanks kumarp......i can't believe i missed that.

I fell into the trap earlier..looking at the figure one can interpret that OP and OQ make a 45 degrees angle with X-axis. But if this is the case then both x and y coordinates should have the same magnitude. Now, coordinates of OP dont have the same magnitude, and that is why our assumption is wrong

So then we have to consider both triangles 30-60-90 triangles separately to find the solution.

hmmm... it is easy with sin and cos stuff... but is that in the GMAT?

if you do not know sin and cos (and parhaps looking for a general solution) try this probably too long of a solution:

1. drop lines down from the two angles which form 90 with the x axis. you get two tirangles. call the two angles at the centre of the cirlce a1 (for the anlge in the left triangle) and b1 (for the right triangle)
2. you know a1 + b1 = 90.
3. this implies a1 = b2 becouse (say for the right triangle) 180 = 90 + 90 - a1 + b2 (the sum of angles).
4. now you have identical triangles as you have 2 equal angles (the 2 90s) and a1 = b2 as well as one equal side (the radius).
5. so s = 1 and t = (3)^(.5) (as the height of the right triangle is the base of the left one and vice versa)

this took me like 10mins to work out... and i am certian i would flop on the exam.

see you

If you can redraw it yourself you can easily find s=1