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?

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