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Problem of this day

Find the radius of the smaller circle.

Note by Indulal Gopal
3 years, 10 months ago

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19 votes

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Using 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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@Ton De Moree exactly Indulal Gopal · 3 years, 10 months ago

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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? 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

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@Sayan Chakraborty Where'd you get 36 and 5? Ryan Wood · 3 years, 10 months ago

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

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@Salmaan Shahid Salman , I think you made an error. Its not 5 cm. Think and do. You can solve it Indulal Gopal · 3 years, 10 months ago

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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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@Daniel Liu but how do you get 36/5 ? Yen Loong · 3 years, 10 months ago

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@Yen Loong From above we can get \(x = \frac{144}{20} = \frac{36}{5}\) Snehdeep Arora · 3 years, 10 months ago

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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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@Sid Silva Nope :) Ton De Moree · 3 years, 10 months ago

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

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@Maharnab Mitra No, it's not. Ton De Moree · 3 years, 10 months ago

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