# Problem of this day

Find the radius of the smaller circle.

Note by Indulal Gopal
5 years, 9 months ago

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

- 5 years, 9 months ago

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

- 5 years, 9 months ago

exactly

- 5 years, 9 months ago

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?

- 5 years, 9 months ago

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

- 5 years, 9 months ago

r = 7.2cm

- 5 years, 9 months ago

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

- 5 years, 9 months ago

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

- 5 years, 9 months ago

Where'd you get 36 and 5?

- 5 years, 9 months ago

1.2

- 5 years, 9 months ago

Nope :)

- 5 years, 9 months ago

7.2 cm.

- 5 years, 9 months ago

7.2 cm

- 5 years, 9 months ago

The answer is not 7.2?

- 5 years, 9 months ago

- 5 years, 9 months ago

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

- 5 years, 9 months ago

but how do you get 36/5 ?

- 5 years, 9 months ago

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

- 5 years, 9 months ago

7.2

- 5 years, 9 months ago

7.2 cm

- 5 years, 9 months ago

7.2

- 5 years, 9 months ago

7.2cm?? or 4.0cm??

- 5 years, 9 months ago

7.2 cm

- 5 years, 9 months ago

7.2 cm

- 5 years, 9 months ago

7.2 cm...

- 5 years, 9 months ago

7.2 cm

- 5 years, 9 months ago

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

- 5 years, 9 months ago

7.2

- 5 years, 9 months ago

3

- 5 years, 9 months ago

7.2 cm

- 5 years, 9 months ago

7.2

- 5 years, 9 months ago

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

- 5 years, 9 months ago

7.2

- 5 years, 9 months ago

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

- 5 years, 9 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

- 5 years, 9 months ago

Similar triangles

7.2 cm

- 5 years, 8 months ago

20/12=12/r r=7.2

- 5 years, 1 month ago

4

- 5 years ago

72

- 5 years ago

7.2 cm

- 5 years ago

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

- 5 years ago

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

- 3 years, 10 months ago

Is the answer 4.8?

- 5 years, 9 months ago

No, it's not.

- 5 years, 9 months ago