On Mon, 27 Aug 2007 11:04:58 +1000, you wrote:
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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/