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

Home > Shapes > Geometry
Objective: Integer! (Posted on 2016-06-14) Difficulty: 3 of 5

O1 is a circle with diameter AOB, of radius r.

C is a point on AB between O and A, and the length of AC is s.

O2 is a second circle, radius t, centred on C, such that s < t < r, so that some part of O2 will always fall outside O1.

D is the common area of O1 and O2.

If r, s, and t are all integer values less than 100 units, say of centimetres, when is D closest to an integer value?

For example, if r=97, s=2, and t=78, then D = 8185.006 cm^2, a near miss. Is there a neater solution than this?

No Solution Yet Submitted by broll    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Interesting | Comment 3 of 4 |

I've checked some of the closer values using my own antiquated method, and my results agree.

The last one is really very close indeed.

Edited on June 15, 2016, 2:49 am
  Posted by broll on 2016-06-15 02:45:45

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

Search body:
Forums (4)
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 - 2020 by Animus Pactum Consulting. All rights reserved. Privacy Information