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?

$</code> ... <code>$</code>...<code>."> Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in $</span> ... <span>$ or $</span> ... <span>$ to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

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

Log in to reply

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

Log in to reply

exactly

Log 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?Log in to reply

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

Log in to reply

r = 7.2cm

Log in to reply

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

Log in to reply

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

Log in to reply

Where'd you get 36 and 5?

Log in to reply

1.2

Log in to reply

Nope :)

Log in to reply

7.2 cm.

Log in to reply

7.2 cm

Log in to reply

The answer is not 7.2?

Log in to reply

radius is 7.2cm

Log in to reply

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

Log in to reply

but how do you get 36/5 ?

Log in to reply

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

Log in to reply

7.2

Log in to reply

7.2 cm

Log in to reply

7.2

Log in to reply

7.2cm?? or 4.0cm??

Log in to reply

7.2 cm

Log in to reply

7.2 cm

Log in to reply

7.2 cm...

Log in to reply

7.2 cm

Log in to reply

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

Log in to reply

7.2

Log in to reply

3

Log in to reply

7.2 cm

Log in to reply

7.2

Log in to reply

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

Log in to reply

7.2

Log in to reply

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

Log in to reply

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

Log in to reply

Similar triangles

7.2 cm

Log in to reply

20/12=12/r r=7.2

Log in to reply

4

Log in to reply

72

Log in to reply

7.2 cm

Log in to reply

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

Log in to reply

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

Log in to reply

Is the answer 4.8?

Log in to reply

No, it's not.

Log in to reply