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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.)
Hints/Tips Comment as discussed earlier | Comment 1 of 4

Please note:

Charlie kindly pointed out that in the given example D = 8184.961 is a closer approximation than 8185.006, if the result is more accurately computed.



  Posted by broll on 2016-06-14 11:12:55
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