## Welcome to BrainDen.com - Brain Teasers Forum

 Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-)
Guest Message by DevFuse

# More triangles in circles

Spoiler for I should have considered two fixed points

Go to the full post

24 replies to this topic

### #1 bonanova

bonanova

bonanova

• Moderator
• 5918 posts
• Gender:Male
• Location:New York

Posted 16 March 2014 - 06:13 AM

While our collective brain trust ponders the nature of triangles defined

by three uniformly random points chosen inside a circle, specifically

the mode of their areas, we ask another question.

Recalling that the mean and median areal coverage of its circle's area are

about 7.4% and 5.4%, what is the probability that a random triangle covers

its circle's center?

• 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #2 Rob_G

Rob_G

Junior Member

• Members
• 29 posts

Posted 24 March 2014 - 04:14 PM

Spoiler for My first thoughts but I don't know where to go from here

• 0

### #3 bonanova

bonanova

bonanova

• Moderator
• 5918 posts
• Gender:Male
• Location:New York

Posted 24 March 2014 - 09:49 PM

Spoiler for My first thoughts but I don't know where to go from here

Sounds like an OK approach. You would need to do some (messy) integrals to account for the points being randomly chosen.

I like to think of this as more of a logic puzzle than a math exercise.

Is there a simpler way to think about the problem?

• 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #4 bonanova

bonanova

bonanova

• Moderator
• 5918 posts
• Gender:Male
• Location:New York

Posted 27 March 2014 - 05:55 AM

Spoiler for Hint

• 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

Senior Member

• Members
• 1702 posts
• Gender:Female

Posted 28 March 2014 - 03:11 PM

Spoiler for my weak thinking

I never get these right but ehh, why not try.

Edited by BMAD, 28 March 2014 - 03:11 PM.

• 0

### #6 bonanova

bonanova

bonanova

• Moderator
• 5918 posts
• Gender:Male
• Location:New York

Posted 28 March 2014 - 07:07 PM

Spoiler for Final clue

• 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #7 Rob_G

Rob_G

Junior Member

• Members
• 29 posts

Posted 28 March 2014 - 08:02 PM

Spoiler for I came up with

Edited by Rob_G, 28 March 2014 - 08:08 PM.

• 0

### #8 bonanova

bonanova

bonanova

• Moderator
• 5918 posts
• Gender:Male
• Location:New York

Posted 30 March 2014 - 08:31 AM

Spoiler for I came up with

It's in that range. Can you nail it down? See my post #6.

• 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

Senior Member

• Members
• 1702 posts
• Gender:Female

Posted 30 March 2014 - 02:36 PM   Best Answer

Spoiler for I should have considered two fixed points

Edited by rookie1ja, 30 March 2014 - 08:50 PM.

• 0

### #10 bonanova

bonanova

bonanova

• Moderator
• 5918 posts
• Gender:Male
• Location:New York

Posted 31 March 2014 - 09:15 PM

This answer is seen to apply for triangles covering the center of any containing shape that has four-fold rotational symmetry, including the circle, such as square and octagon.

Does to hold for triangles contained by other shapes, say a pentagon?

• 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#### 0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users