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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    
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Comments: ( Back to comment list | You must be logged in to post comments.)
re: Interesting Comment 4 of 4 |
(In reply to Interesting by broll)

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

by changing the selection line to

  If Abs(d - dround) <= 0.00001 Then

  Posted by Charlie on 2016-06-15 07:44:09
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