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 Objective: Integer! (Posted on 2016-06-14)

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

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