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 I've Been Working... (Posted on 2004-01-07)
Between Massena and Anaheim there are two railroad tracks. One of them is straight and is 4 miles long. The other one is the arc of a circle and is 5 miles long.

What is the radius of curvature of the curved track?

 No Solution Yet Submitted by DJ Rating: 4.0000 (7 votes)

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From the problem,  we get an arch A of length 5 whose endpoints are connected by a straight line B of length 4. Supposing O to be centre of curvature, we make an  isocelles triangle whose equal sides are each  of length l and the base is B=4. Let x (inradians) be the angle at  O. So we get two unknowns : x and l (which is also radius ofcurvature). And we have  two equations:

x*l=5 --->(a)

sin(x/2) =  2/l --->(b)    [since we have an isocelles triangle]

solving, we get l  which  is required

 Posted by Okash Khuwajo on 2005-06-18 12:22:04

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