Problem of this day

Find the radius of the smaller circle.

Note by Indulal Gopal
6 years ago

No vote yet
19 votes

  Easy Math Editor

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.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

Using Basic proportionality theorem r12=1220r=14420=7.2\frac{r}{12} = \frac{12}{20} \Rightarrow r = \frac{144}{20} = \boxed{7.2}

Snehdeep Arora - 6 years ago

Log in to reply

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

Ton de Moree - 6 years ago

Log in to reply

exactly

indulal gopal - 6 years ago

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+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 - 6 years ago

Log in to reply

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

Yen Loong - 6 years ago

Log in to reply

r = 7.2cm

salmaan shahid - 6 years ago

Log in to reply

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

indulal gopal - 6 years ago

Log in to reply

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

Sayan Chakraborty - 6 years ago

Log in to reply

Where'd you get 36 and 5?

Ryan Wood - 5 years, 12 months ago

Log in to reply

1.2

Sid Silva - 6 years ago

Log in to reply

Nope :)

Ton de Moree - 6 years ago

Log in to reply

7.2 cm.

Lim S. - 6 years ago

Log in to reply

7.2 cm

Kunal Rmth - 6 years ago

Log in to reply

The answer is not 7.2?

Log in to reply

radius is 7.2cm

Ravi Teja - 6 years ago

Log in to reply

...Well... 1220=x12x=365\dfrac{12}{20}=\dfrac{x}{12}\Rightarrow x=\boxed{\dfrac{36}{5}}. Waaay too simple.

Daniel Liu - 6 years ago

Log in to reply

but how do you get 36/5 ?

Yen Loong - 6 years ago

Log in to reply

From above we can get x=14420=365x = \frac{144}{20} = \frac{36}{5}

Snehdeep Arora - 6 years ago

Log in to reply

7.2

Adeeb Zaman - 6 years ago

Log in to reply

7.2 cm

Log in to reply

7.2

Jarrar Hassan - 6 years ago

Log in to reply

7.2cm?? or 4.0cm??

Philips Zephirum Lam - 6 years ago

Log in to reply

7.2 cm

Shohidul Islam - 6 years ago

Log in to reply

7.2 cm

Priyank Agarwal - 6 years ago

Log in to reply

7.2 cm...

Prathamesh Kulkarni - 6 years ago

Log in to reply

7.2 cm

bobby jim - 6 years ago

Log in to reply

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

Yen Loong - 6 years ago

Log in to reply

7.2

Aditya Singh - 6 years ago

Log in to reply

3

AnNan Khan - 6 years ago

Log in to reply

7.2 cm

Tan Li Xuan - 6 years ago

Log in to reply

7.2

Rudresh Trivedi - 6 years ago

Log in to reply

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

Rajarshi Chatterjee - 6 years ago

Log in to reply

7.2

Yunus Arefin - 6 years ago

Log in to reply

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

Arnav Rupde - 5 years, 12 months ago

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

Gabriel Falcão Dos Santos - 5 years, 12 months ago

Log in to reply

Similar triangles

7.2 cm

SABAB AHAD - 5 years, 11 months ago

Log in to reply

20/12=12/r r=7.2

nabila ahmed - 5 years, 4 months ago

Log in to reply

4

Sumeet Saini - 5 years, 3 months ago

Log in to reply

72

Sumeet Saini - 5 years, 3 months ago

Log in to reply

7.2 cm

Sumeet Saini - 5 years, 3 months ago

Log in to reply

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

Yash Mirani - 5 years, 3 months ago

Log in to reply

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

Hadia Qadir - 4 years, 1 month ago

Log in to reply

Is the answer 4.8?

Maharnab Mitra - 6 years ago

Log in to reply

No, it's not.

Ton de Moree - 6 years ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...