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# Two spherical balls lie on the ground touching. If one of

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Two spherical balls lie on the ground touching. If one of  [#permalink]

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19 May 2011, 07:31
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Difficulty:

65% (hard)

Question Stats:

54% (03:50) correct 46% (02:30) wrong based on 42 sessions

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Two spherical balls lie on the ground touching. If one of the balls has a radius of 8 cm, and the point of contact is 10 cm above the ground, what is the radius of the other ball?

(A) 18 cm
(B) 40/3 cm
(C) 25/2 cm
(D) 13 cm
(E) none of the these

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Re: Two spherical balls lie on the ground touching  [#permalink]

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19 May 2011, 10:01
2
See the attached image. smaller circle has radius 8. Consider two triangle. One with hypotenuse 8 and another with hypotenuse 8+x

In smaller triangle, sides are $$8,2,2\sqrt{15}$$
sin@ = 2/8=1/4

In larger triangle, sides are $$8+x, 2\sqrt{15}+10, x-8$$
sin@= x-8/x+8
1/4=x-8/x+8
x=40/3.
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img.JPG [ 10.47 KiB | Viewed 5171 times ]

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Re: Two spherical balls lie on the ground touching  [#permalink]

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21 May 2011, 01:08
similar triangle properties..

2/r+8 = 8/r-8

giving r = 40/3.
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Re: Two spherical balls lie on the ground touching  [#permalink]

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12 Jun 2011, 16:35
How do we know the line joining the two centre's passes through the point of intersection of the two circles?.

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Re: Two spherical balls lie on the ground touching  [#permalink]

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12 Jun 2011, 19:34
1
maheshsrini wrote:
How do we know the line joining the two centre's passes through the point of intersection of the two circles?.

For the moment, just think of the two circles touching each other at point, say P, as shown in the diagram in the post by jamifahad.

Now, say, you draw a tangent at P, the point of intersection. This will be a common tangent to both the circles at the point P. Join the center of each circle with P. We know that the line joining the center to the point of tangency will be perpendicular to the tangent.
Hence they will form an angle of 180 degrees and will therefore be straight.
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Re: Two spherical balls lie on the ground touching  [#permalink]

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12 Jun 2011, 22:22
hussi9 wrote:
Two spherical balls lie on the ground touching. If one of the balls has a radius of 8 cm, and the point of contact is 10 cm above the ground, what is the radius of the other ball?

(1) 18 cm (2) 40/3 cm (3) 25/2 cm (4) 13 cm (5) none of the these

I think using similar triangle property is the best
From the diagram below , we know
triangle CDA is similar triangle BEA
therefore
BE/EA= CD/DA..... (DA is the radius we are looking for)
2/8 = (r-8)/(r+8)
solve to get r = 40/3
Attachments

circle.jpg [ 14.38 KiB | Viewed 4784 times ]

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Re: Two spherical balls lie on the ground touching  [#permalink]

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13 Jun 2011, 08:01
yeah, got it. Thanks Karishma.
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Re: Two spherical balls lie on the ground touching. If one of  [#permalink]

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08 Jul 2017, 05:16
I have a query.
In the ques it it stated that "the point of contact is 10 cm above the ground". But in the images of solutions proposed, the value 10 is suggested as distance between point of contacts of circles with the ground.
Can someone clarify what I am missing in comprehending the problem?
Re: Two spherical balls lie on the ground touching. If one of   [#permalink] 08 Jul 2017, 05:16
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