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Math Problem - Help needed to solve

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by priyasaibaba » Wed Apr 21, 2010 7:08 am
Can anyone help me solve this problem?

As the figure above shows, two circles lie on a line and tangent to each other. If the radius of two circles are 2r and r, respectively, in terms of r, AB=?
(A) 5r/2
(B) 8r/3
(C) 2*2^1/2*r
(D) 3r
(E) 2*3^1/2*r

Pls find the figure in the attached doc.

Thanks for your help.
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by eaakbari » Wed Apr 21, 2010 7:33 am
Do attach the figure, you will not be able to paste it. I cannot understand the figure solely through your explanation
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by priyasaibaba » Wed Apr 21, 2010 7:46 am
Hi eaakbari, I have attached the figure. Pls let me know, if u find the answer.

Thanks,
Priya
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by priyasaibaba » Wed Apr 21, 2010 7:53 am
D is not the answer. C is the answer. Can someone explain the steps to get the answer?
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by eaakbari » Wed Apr 21, 2010 7:55 am
Answer is C. wait let me explain
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by eaakbari » Wed Apr 21, 2010 8:10 am
Image

CD is a line joining the 2 centers
ED is a line parallel and equal to AB which meets line AC at point E

Now CD = 2r + r = 3r
CE = CA-EA = 2r - r = r

Hence Using pythogoras

ED^2 = 9r^2 + r^2
ED = AB = ROOT(8r^2)
= 2root2 * r

HTH
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by akhpad » Wed Apr 21, 2010 8:22 am
Correct, C is the answer
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by priyasaibaba » Wed Apr 21, 2010 8:22 am
Wow, thanks very much. Appreciate your help.
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by pkw209 » Wed Apr 21, 2010 4:56 pm
good problem. Haven't come across one like that yet.
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by pkw209 » Wed Apr 21, 2010 4:56 pm
...until now
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by Stuart@KaplanGMAT » Wed Apr 21, 2010 10:08 pm
eaakbari wrote:Image

CD is a line joining the 2 centers
ED is a line parallel and equal to AB which meets line AC at point E

Now CD = 2r + r = 3r
CE = CA-EA = 2r - r = r

Hence Using pythogoras

ED^2 = 9r^2 + r^2
ED = AB = ROOT(8r^2)
= 2root2 * r

HTH
Great job!

You ended up with the correct answer, just want to correct one small typo so no one gets confused along the way:
ED^2 = 9r^2 + r^2
9(r^2) is actually the hypotenuse, not ED^2, so that should be:

ED^2 = 9(r^2) - r^2

You did the math as though it were a subtraction sign, so all is good after that point!
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