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?
–
Priyank Agarwal
·
3 years, 10 months ago

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@Priyank Agarwal
–
but just have a little hard to understand your formula...
–
Yen Loong
·
3 years, 10 months ago

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N ths is a prblm -_-
Simply,36/5 gives 7.2
–
Sayan Chakraborty
·
3 years, 10 months ago

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
–
Gabriel Falcão Dos Santos
·
3 years, 10 months ago

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use basic proportionality theorem r/12=12/20 r=7.2
–
Arnav Rupde
·
3 years, 10 months ago

## Comments

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TopNewestUsing Basic proportionality theorem \(\frac{r}{12} = \frac{12}{20} \Rightarrow r = \frac{144}{20} = \boxed{7.2}\) – Snehdeep Arora · 3 years, 10 months ago

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Once you find the like triangles it's not that hard anymore :) – Ton De Moree · 3 years, 10 months ago

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– Indulal Gopal · 3 years, 10 months ago

exactlyLog in to reply

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? – Priyank Agarwal · 3 years, 10 months agoLog in to reply

– Yen Loong · 3 years, 10 months ago

but just have a little hard to understand your formula...Log in to reply

N ths is a prblm -_- Simply,36/5 gives 7.2 – Sayan Chakraborty · 3 years, 10 months ago

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– Ryan Wood · 3 years, 10 months ago

Where'd you get 36 and 5?Log in to reply

r = 7.2cm – Salmaan Shahid · 3 years, 10 months ago

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– Indulal Gopal · 3 years, 10 months ago

Salman , I think you made an error. Its not 5 cm. Think and do. You can solve itLog in to reply

20:12 = 5:3 12:r = 5:3 r = 3:5 x 12 r = 7,2 what a simple – Hadia Qadir · 1 year, 11 months ago

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Just basic proportionality funda and you are through. r/12=12/20 r=7.2cm – Yash Mirani · 3 years, 1 month ago

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7.2 cm – Sumeet Saini · 3 years, 1 month ago

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72 – Sumeet Saini · 3 years, 1 month ago

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4 – Sumeet Saini · 3 years, 1 month ago

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20/12=12/r r=7.2 – Nabila Ahmed · 3 years, 2 months ago

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Similar triangles

7.2 cm – Sabab Ahad · 3 years, 9 months ago

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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 – Gabriel Falcão Dos Santos · 3 years, 10 months ago

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use basic proportionality theorem r/12=12/20 r=7.2 – Arnav Rupde · 3 years, 10 months ago

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7.2 – Yunus Arefin · 3 years, 10 months ago

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It is too easy to be the problem of the day .r=7.2cm – Rajarshi Chatterjee · 3 years, 10 months ago

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7.2 – Rudresh Trivedi · 3 years, 10 months ago

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7.2 cm – Tan Li Xuan · 3 years, 10 months ago

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3 – AnNan Khan · 3 years, 10 months ago

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7.2 – Aditya Singh · 3 years, 10 months ago

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I think the proper answer is 7.2cm if I no mistaken... – Yen Loong · 3 years, 10 months ago

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7.2 cm – Bobby Jim · 3 years, 10 months ago

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7.2 cm... – Prathamesh Kulkarni · 3 years, 10 months ago

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7.2 cm – Priyank Agarwal · 3 years, 10 months ago

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7.2 cm – Shohidul Islam · 3 years, 10 months ago

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7.2cm?? or 4.0cm?? – Philips Zephirum Lam · 3 years, 10 months ago

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7.2 – Jarrar Hassan · 3 years, 10 months ago

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7.2 cm – Ram Prakash Patel Patel · 3 years, 10 months ago

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7.2 – Adeeb Zaman · 3 years, 10 months ago

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...Well... \(\dfrac{12}{20}=\dfrac{x}{12}\Rightarrow x=\boxed{\dfrac{36}{5}}\). Waaay too simple. – Daniel Liu · 3 years, 10 months ago

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– Yen Loong · 3 years, 10 months ago

but how do you get 36/5 ?Log in to reply

– Snehdeep Arora · 3 years, 10 months ago

From above we can get \(x = \frac{144}{20} = \frac{36}{5}\)Log in to reply

radius is 7.2cm – Ravi Teja · 3 years, 10 months ago

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The answer is not 7.2? – Diego E. Nazario Ojeda · 3 years, 10 months ago

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7.2 cm – Kunal Rmth · 3 years, 10 months ago

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7.2 cm. – Lim S. · 3 years, 10 months ago

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1.2 – Sid Silva · 3 years, 10 months ago

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– Ton De Moree · 3 years, 10 months ago

Nope :)Log in to reply

Is the answer 4.8? – Maharnab Mitra · 3 years, 10 months ago

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– Ton De Moree · 3 years, 10 months ago

No, it's not.Log in to reply