SOLUTION OF TRIANGLES/.....

A point O is situated on a circle of radius R. With centre O, another circle of radius 3R/2 is described. Inside the crescent shaped area intercepted between these circles, a circle of radius R/8 is placed. If the same circle moves in contact with the original circle of radius R, find the length of the arc described by its centre in moving from one extreme position to the other.

#HelpMe!

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.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered 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"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

It's not a problem posted on Brilliant, otherwise I would have shut it down already. I am unaware if it's a current contest problem.

The statement of the problem could be better explained.

A quick search shows that this problem has used in several contexts, and I see an attribution to Loney [problem 81 of this pdf].

Calvin Lin Staff - 8 years, 4 months ago

I'm now wondering either this is a contest problem or this week's Brilliant Problem. (It is posted two times already.)

Zi Song Yeoh - 8 years, 4 months ago

its not a problem posted on brilliant.......... but is there a rule that we need to post only brilliant questions :((((

Ayushi Agrawal - 8 years, 4 months ago

Ayushi,

It just seems a lot like a problem that would be on Brilliant. The rules are, you cannot post a problem on a current Brilliant problem set, your homework, or questions on an exam/test. We also ask that you cite a source when you post word for word a problem that you did not make up yourself.

To avoid confusing people a good practice would be to state in the discussion body where you found the problem, and why you think it is interesting. This context, will make people more excited to solve the problem. People are not just interested in solving the problem they are also interested in why you think it is cool and wanted to share it:)

Peter Taylor Staff - 8 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$