All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes
Circular Fun (Posted on 2005-07-28) Difficulty: 2 of 5
When you draw three circles of radius r such that all three are externally tangent, what is the area of the shape in the center in terms of r?

See The Solution Submitted by Justin    
Rating: 3.2857 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Requested solution Comment 18 of 18 |

Sorry, but they don't seem to want to activate the solution link.

sqrt(3)r^2-pi(r^2)/2

This solution is achieved by drawing simple math.

Take the distance between the centers of two circles (2r) and make it into the sides of an equilateral triangle.

You now find the height of the triangle: sqrt((2r)^2-(r^2)) = sqrt(3)r.

Now find the area of the triangle by subbing in sqrt(3)r as h. b=2r, so A=2sqrt(3)r^2/2 so A=sqrt(3)r^2.

Subtract the three sixths of the circles(each angle is 60 degrees), to get sqrt(3)r^2-pi(r^2)/2.


  Posted by Justin on 2006-01-20 09:09:02
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information