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I converted it into a problem of Straight Lines.
Mapping the distance of the centre of a sphere from the topmost point on the y axis , and radius on the x axis,
I calculated slope by calculating dy/dx of the given 2 spheres as (52-20)/(12-20) = -4 .
Then using the equation of straight line y=mx+c and putting the value of y=52 and x=12, 52=(-4)x12 +c, c comes out to be 100. Then for the unknown radius , we know y=64+r and x=r. Solving this 64+r=(-4) x r +100 which gives r=7.2........ Cool approach, isn't it?

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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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## Comments

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TopNewestUsing Basic proportionality theorem $\frac{r}{12} = \frac{12}{20} \Rightarrow r = \frac{144}{20} = \boxed{7.2}$

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Once you find the like triangles it's not that hard anymore :)

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exactly

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I converted it into a problem of Straight Lines. Mapping the distance of the centre of a sphere from the topmost point on the y axis , and radius on the x axis, I calculated slope by calculating dy/dx of the given 2 spheres as (52-20)/(12-20) = -4 . Then using the equation of straight line

y=mx+cand putting the value of y=52 and x=12, 52=(-4)x12 +c, c comes out to be 100. Then for the unknown radius , we know y=64+r and x=r. Solving this 64+r=(-4) x r +100 which gives r=7.2........ Cool approach, isn't it?Log in to reply

but just have a little hard to understand your formula...

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r = 7.2cm

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Salman , I think you made an error. Its not 5 cm. Think and do. You can solve it

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N ths is a prblm -_- Simply,36/5 gives 7.2

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Where'd you get 36 and 5?

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1.2

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Nope :)

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7.2 cm.

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7.2 cm

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The answer is not 7.2?

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radius is 7.2cm

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...Well... $\dfrac{12}{20}=\dfrac{x}{12}\Rightarrow x=\boxed{\dfrac{36}{5}}$. Waaay too simple.

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but how do you get 36/5 ?

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From above we can get $x = \frac{144}{20} = \frac{36}{5}$

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7.2

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7.2 cm

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7.2

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7.2cm?? or 4.0cm??

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7.2 cm

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7.2 cm

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7.2 cm...

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7.2 cm

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I think the proper answer is 7.2cm if I no mistaken...

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7.2

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3

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7.2 cm

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7.2

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It is too easy to be the problem of the day .r=7.2cm

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7.2

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use basic proportionality theorem r/12=12/20 r=7.2

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This problem can be resolved by using Geometric progression. The rays are in G.P. . So 20/12=5/3 it's the common ratio. 12/5/3= 7,2=r

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Similar triangles

7.2 cm

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20/12=12/r r=7.2

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4

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72

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7.2 cm

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Just basic proportionality funda and you are through. r/12=12/20 r=7.2cm

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20:12 = 5:3 12:r = 5:3 r = 3:5 x 12 r = 7,2 what a simple

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Is the answer 4.8?

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No, it's not.

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