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GEOMETRY

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GEOMETRY

by CSASHISHPANDAY » Wed Sep 19, 2012 10:32 pm
In the figure attached, the length of segment xz is 24. What is the circumference of the circle with diameter wy ?
1.The length of segment wx is 40.
2.The length of segment xy is 30.
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by KapilKapoor » Wed Sep 19, 2012 10:50 pm
Hi,

As wy is diameter (d), triangle wxy is right angled triangle. so

1/2* wy * xz = 1/2 * wx * xy
1/2* d * 24 = 1/2 * wx * xy ----1

Moreover d = wz + zy ----2

Stmt 1: wx = 40
=> wz = 32 (sqrt(40^2-24^2))
Assume xy = p
Putting values in equ(2)
32 + sqrt(p^2-24^2) = d ----3
Putting values in equ(1)
d/2*24 = 1/2*40*p ----4

By solving 3,4 we can get p,d.
d=50
Hence Stmt 1 is sufficient.

In the similar way Stmt 2 is also sufficient.

Hence the answer is D

Thanks & Regards,
Kapil
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by anjalimanas » Wed Nov 21, 2012 1:21 am
Is there an easier / faster way to solve this problem. as i think it is a DS problem. thanks
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by Bill@VeritasPrep » Wed Nov 21, 2012 9:43 am
anjalimanas wrote:Is there an easier / faster way to solve this problem. as i think it is a DS problem. thanks
If you recognize that you can set up the Pythagorean theorem 3 times (once for each of the smaller triangles and once for the big triangle), then you should see that you're left with two unknowns: WZ and ZY. Since each statement fills in one of your unknowns, you can then solve for the other and find the diameter. You don't actually have to do the math.
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