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?

Since the program shows only new record breakers, some close fits are not shown, such as the other four of these:

 r  t  s           D
73 22  2     798.999999050828
74 43 42    5790.00000154383
84 43 39    5674.00000983413
86 83 68   19360.0000031004
95 85 74   21314.0000033145