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

Home > Shapes > Geometry
Two circles (Posted on 2004-10-21) Difficulty: 3 of 5
In a 8½x11 sheet of paper I drew two equal non-overlapping circles -- both completely inside the paper, of course.

What's the largest portion of the paper I could cover with the circles?

What would be the answer if I drew THREE equal circles?

No Solution Yet Submitted by Federico Kereki    
Rating: 3.2500 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Question re(2): Two circles case--further explanation | Comment 7 of 11 |
(In reply to re: Two circles case--further explanation by Charlie)

I think I agree with putting the circles in opposite corners and then expanding them until they are tangent to each other AND tangent to the sides of the paper.  Their centers being on 45 degree angles from the corners, but their tangent point will not be on this same line, but I guess we don't care. Working from center to center, we know:

(2r)^2 = (8.5-2r)^2 + (11-2r)^2

Here's were I don't follow. When I expand this, I get:

4r^2 = (8.5)^2 - 17r + 4r^2 + (11)^2 - 22r + 4r^2
4r^2 = 8r^2 - 39r + (8.5)^2 + (11)^2
0 = 4r^2 - 39r + (8.5)^2 + (11)^2,  My question is where did your -78r term come from?

I would much rather have the 78, because when I plug my numbers into the quadratic formula, I end up having to take the square root of a neg number.

  Posted by bob909 on 2004-10-22 09:09:41

Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information