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A, B and C are three points on a plane such that AB = BC = 1 and CA = sqrt 3. Draw three circles whose diameters are AB, BC and CA respectively. The area of the region included in all three circles (the grey region below) is (a/b)pi + (sqrt c /d) in simplest form, so a, b, c, d are positive integers, a and b are relatively prime, and c is not divisible by the square of a prime. Enter the values of a, b, c, d in order, separating by commas.

Picture: https://latex.artofproblemsolving.com/9/f/e/9fe0a447f9c035e61fc690f618e76a639d7fdd2c.png

 Feb 19, 2023
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(a,b,c,d) = (8,3,-5,3)

 Feb 19, 2023

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