Steve Schafer wrote:
x = a - sqrt(a^2 - b^2)
I don't know offhand if there's a straightforward way to arrive at this result without using trigonometry.
Here you go, though with a slightly different result (same as Joel Koerwer): a^2=(b^2)/4+(a-x)^2 (Pythagoras) solving x: --> x(1,2) = a +/- sqrt (a^2 - b^2/4) (I) Did anyone compare the answers? (I) aai a b = (x1,x2) where x1 = a + sqrt disc x2 = a - sqrt disc disc = a^2-b^2/4 Others: schafer a b = a - sqrt(a^2 - b^2) jedaï a b = a * (1 - cos (b/(2*a))) stefan a b = a - a * sqrt (1 - b*b / a*a) joel a b = a - sqrt (a*a - b*b/4) Assume a and b are given: a=10; b=8 Results: *Main> aai 10 8 (19.165151389911678,0.8348486100883203) the answer is the smaller value the other value = the diameter of the circumference minus x (0.00 secs, 523308 bytes) *Main> schafer 10 8 4.0 (0.01 secs, 524924 bytes) *Main> jedaï 10 8 0.789390059971149 (0.01 secs, 524896 bytes) *Main> stefan 10 8 NaN (0.00 secs, 524896 bytes) *Main> stefan 10 8 4.0 (0.01 secs, 524896 bytes) *Main> joel 10 8 0.8348486100883203 (0.01 secs, 524896 bytes) Where do I go wrong (I)? Thanks @@i