(PLEASE SOLVE THIS PROBLEM, ANYONE!) PS Problem #5. Thx!!

Question

In the figure above, P and O 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

It comes from GMATPrep. Thanks!

Aleehsgonji · Answer

This problem was solved earlier. The link is what-is-the-value-of-t-81370.html

sudiptak · Answer

consider the centre of the circle is at O(0,0).

Since OP and OQ are the radius of the circle 
therefore OP=OQ
or, (\sqrt{3})^2+ (1)2 = s^2 + t^2
therefore s^2+t^2 = 4 ...................(1)

again , since POQ is 90 degrees. OP and OQ are perpendicular. hence product of their slopes =-1.
slope of Q = t/s
slope of P = -1/\sqrt{3}
therefore, (t/s)*   = -1
so, t/s = \sqrt{3}
or, t^2 = 3s^2 ....................(2)

solving (1) & (2) we get s = +/- (1). But , since Q is in first quadrant, s = 1 , hence t = \sqrt{3}

jallenmorris · Answer

I'm not sure how the other forum solved it, but here is another way to approach the problem.

If you look at the slope of a line and realize that because we're told the two lines are 90 degrees from each other, you know the lines are perpendicular.

so what ist he slope of a line?  y = \frac{1}{3}x + 0  Sure we don't need the + 0, but it helps to see all the parts there.

Now I used 1/3, but that's just a number to show the formula for a line.

If the coordinates we do know were used to determine the slope of the line, what would the equation look like?

y = -\frac{1}{\sqrt{3}}x + 0

It's a negative because the slope runs from top left to bottom right and those lines are always negative. So if we know the slope, then how would we figure what the slope is of the perpendicular line, with point {s,t}?

Invert and negate the slope. We can use the same exact numbrs because we know the line is the radius of a circle and therefore the same length. By using the same numbers, we know that it will be the same length and be the correct values for {s,t}

so inverted the slope becomes  \frac{\sqrt{3}}{1}x

Now if before we had  sqrt{3}  on bottom, and it was the x value, and now it is on top, it will not be the x value, but the y value, which corresponds to  t .

Hope this helps present a different way of looking at it. Answering the question won't take nearly as long as exlaining it.

travern · Answer

all you need to determine is that a 30-60-90 triangle can be fitted with OQ as hypotenuse

jallenmorris · Answer

what part of the picture provided lets you determine the angle measurements? I realize you can see that the readius is 2 from the numbers provided in the first point, but you still have to address how the 90 degree angle between the lines figures intot he problem.

(PLEASE SOLVE THIS PROBLEM, ANYONE!) PS Problem #5. Thx!!

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