On Mon, 27 Aug 2007 11:04:58 +1000, you wrote: >-----BEGIN PGP SIGNED MESSAGE----- >Hash: SHA1 > >I went camping on the weekend and a friend of mine who is a builder >asked me many questions on geometry as they apply to his every day work >- - most of which I could answer. > >However, there was one that I couldn't and I am having trouble googling >a solution (for lack of keywords?). I'm hoping a fellow Haskeller could >help me out (in Haskell of course). > >The problem is finding the unknown x from the two knowns a and b in the >given image below (excuse my Microsoft Paintbrush skills). I may have >misunderstood his problem (we were drawing in dirt) and actually, it is >the straight line between the two points on the circumference that are >known and not the specified 'b', but I figure I could derive one >solution from another if I have misunderstood him. > >Here is my image: >http://tinyurl.com/2kgsjy > >Thanks for any tips or keywords with which to google!
So a is the radius of the circle, and b is half the length of the chord. From basic trigonometry: b = a * sin @ where @ is half of the angle between the two radii as drawn in the picture. Then: x = a * (1 - cos @) Using the trigonometric identity sin^2 @ + cos^2 @ = 1 and rearranging, we get: 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. By the way, I found http://www.1728.com/circsect.htm by Googling height chord. Steve Schafer Fenestra Technologies Corp. http://www.fenestra.com/ _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe